Indagationes Mathematicae-New Series最新文献

{"title":"Some remarks on the smash-nilpotence conjecture","authors":"Bruno Kahn","doi":"10.1016/j.indag.2024.05.009","DOIUrl":"10.1016/j.indag.2024.05.009","url":null,"abstract":"<div><div>We discuss cases where Voevodsky’s smash nilpotence conjecture is known, and give a few new ones. In particular we explain a theorem of the cube for 1-cycles, which is due to Oussama Ouriachi.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 1","pages":"Pages 137-148"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141553293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Virtual localization in equivariant Witt cohomology","authors":"Marc Levine","doi":"10.1016/j.indag.2024.11.005","DOIUrl":"10.1016/j.indag.2024.11.005","url":null,"abstract":"<div><div>We prove an analog of the virtual localization theorem of Graber–Pandharipande, in the setting of an action by the normalizer of the torus in <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and with the Chow groups replaced by the cohomology of a suitably twisted sheaf of Witt groups.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 1","pages":"Pages 303-375"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weil cohomology theories and their motivic Hopf algebroids","authors":"Joseph Ayoub","doi":"10.1016/j.indag.2024.09.009","DOIUrl":"10.1016/j.indag.2024.09.009","url":null,"abstract":"<div><div>In this paper we discuss a general notion of Weil cohomology theories, both in algebraic geometry and in rigid analytic geometry. We allow our Weil cohomology theories to have coefficients in arbitrary commutative ring spectra. Using the theory of motives, we give three equivalent viewpoints on Weil cohomology theories: as a cohomology theory on smooth varieties, as a motivic spectrum and as a realization functor. We also associate to every Weil cohomology theory a motivic Hopf algebroid generalizing the construction we gave in Ayoub (2014) for the Betti cohomology. Exploiting results and constructions from Ayoub (2020), we are able to prove that the motivic Hopf algebroids of all the classical Weil cohomology theories are connective. In particular, they give rise to motivic Galois groupoids which are spectral affine groupoid schemes.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 1","pages":"Pages 195-249"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiresolution analysis on spectra of Hermitian matrices","authors":"Lukas Langen,&nbsp;Margit Rösler","doi":"10.1016/j.indag.2025.03.009","DOIUrl":"10.1016/j.indag.2025.03.009","url":null,"abstract":"<div><div>We establish a multiresolution analysis on the space <span><math><mrow><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> of <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> complex Hermitian matrices which is adapted to invariance under conjugation by the unitary group <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span> The orbits under this action are parametrized by the possible ordered spectra of Hermitian matrices, which constitute a closed Weyl chamber of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. The space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mrow><mo>(</mo><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msup></mrow></math></span> of radial, <em>i.e</em>. <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span>-invariant <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-functions on <span><math><mrow><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> is naturally identified with a certain weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-space on this chamber.</div><div>The scale spaces of our multiresolution analysis are obtained by usual dyadic dilations as well as generalized translations of a scaling function, where the generalized translation is a hypergroup translation which respects the radial geometry. We provide a concise criterion to characterize orthonormal wavelet bases and show that such bases always exist. They provide natural orthonormal bases of the space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mrow><mo>(</mo><mtext>Herm</mtext><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>U</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msup><mo>.</mo></mrow></math></span> Furthermore, we show how to obtain radial scaling functions from classical scaling functions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Finally, generalizations related to the Cartan decompositions for general compact Lie groups are indicated.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1671-1694"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Induction for representations of coideal doubles, with an application to quantum SL(2,R)","authors":"K. De Commer","doi":"10.1016/j.indag.2025.03.004","DOIUrl":"10.1016/j.indag.2025.03.004","url":null,"abstract":"<div><div>We investigate the theory of induction in the setting of doubles of coideal <span><math><mo>∗</mo></math></span>-subalgebras of compact quantum group Hopf <span><math><mo>∗</mo></math></span>-algebras. We then exemplify parts of this theory in the particular case of quantum <span><math><mrow><mi>S</mi><mi>L</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, and compute the decomposition of the regular representation for quantum <span><math><mrow><mi>S</mi><mi>L</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> into irreducibles.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1628-1670"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dunkl symmetric coherent pairs of measures. An application to Fourier Dunkl–Sobolev expansions","authors":"Mabrouk Sghaier ,&nbsp;Francisco Marcellán ,&nbsp;Sabrine Hamdi","doi":"10.1016/j.indag.2025.01.006","DOIUrl":"10.1016/j.indag.2025.01.006","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be the Dunkl operator. A pair of symmetric measures &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; supported on a symmetric subset of the real line is said to be a symmetric Dunkl-coherent pair if the corresponding sequences of monic orthogonal polynomials &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (resp.) satisfy &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt; is a sequence of non-zero complex numbers and &lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;In this contribution we focus the attention on the sequence &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of monic orthogonal polynomials with respect to the Dunkl–Sobolev inner product &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1513-1532"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exponentially-improved asymptotics for q-difference equations: 2ϕ0 and qPI","authors":"Nalini Joshi ,&nbsp;Adri Olde Daalhuis","doi":"10.1016/j.indag.2025.02.002","DOIUrl":"10.1016/j.indag.2025.02.002","url":null,"abstract":"<div><div>Usually when solving differential or difference equations via series solutions one encounters divergent series in which the coefficients grow like a factorial. Surprisingly, in the <span><math><mi>q</mi></math></span>-world the <span><math><mi>n</mi></math></span>th coefficient is often of the size <span><math><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>n</mi><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup></math></span>, in which <span><math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is fixed. Hence, the divergence is much stronger, and one has to introduce alternative Borel and Laplace transforms to make sense of these formal series. We will discuss exponentially-improved asymptotics for the basic hypergeometric function <span><math><mrow><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> and for solutions of the <span><math><mi>q</mi></math></span>-difference first Painlevé equation <span><math><mrow><mi>q</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub></mrow></math></span>. These are optimal truncated expansions, and re-expansions in terms of new <span><math><mi>q</mi></math></span>-hyperterminant functions. The re-expansions do incorporate the Stokes phenomena.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1555-1571"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An explicit formula for free multiplicative Brownian motions via spherical functions","authors":"Martin Auer,&nbsp;Michael Voit","doi":"10.1016/j.indag.2025.03.010","DOIUrl":"10.1016/j.indag.2025.03.010","url":null,"abstract":"<div><div>After some normalization, the logarithms of the ordered singular values of Brownian motions on <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>=</mo><mi>R</mi><mo>,</mo><mi>ℂ</mi></mrow></math></span> form Weyl-group invariant Heckman–Opdam processes on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>. We use classical elementary formulas for the spherical functions of <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow><mo>/</mo><mi>S</mi><mi>U</mi><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> and the associated Euclidean spaces <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span> of Hermitian matrices, and show that in the <span><math><mrow><mi>G</mi><mi>L</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span>-case, these processes can be also interpreted as ordered eigenvalues of Brownian motions on <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span> with particular drifts. This leads to an explicit description for the free limits for the associated empirical processes for <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> where these limits are independent from the parameter <span><math><mi>k</mi></math></span> of the Heckman–Opdam processes. In particular we get new formulas for the distributions of the free multiplicative Brownian motion of Biane. We also show how this approach works for the root systems <span><math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1695-1716"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orthogonality of very well-poised series","authors":"Mourad E.H. Ismail ,&nbsp;Eric M. Rains ,&nbsp;Dennis Stanton","doi":"10.1016/j.indag.2024.09.007","DOIUrl":"10.1016/j.indag.2024.09.007","url":null,"abstract":"<div><div>Rodrigues formulas for very well-poised basic hypergeometric series of any order are given. Orthogonality relations are found for rational functions with an arbitrary number of parameters which generalize the Askey–Wilson polynomials and Rahman’s <span><math><mrow><msub><mrow><mspace></mspace></mrow><mrow><mn>10</mn></mrow></msub><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>9</mn></mrow></msub></mrow></math></span> biorthogonal rational functions. A pair of orthogonal rational functions of type <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>I</mi><mi>I</mi></mrow></msub></math></span> is identified. Elliptic analogues of some of these results are also included.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1493-1512"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A family of orthogonal functions on the unit circle and a new multilateral matrix inverse","authors":"Michael J. Schlosser","doi":"10.1016/j.indag.2025.05.010","DOIUrl":"10.1016/j.indag.2025.05.010","url":null,"abstract":"<div><div>Using Bailey’s very-well-poised <span><math><mrow><msub><mrow></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mi>ψ</mi></mrow><mrow><mn>6</mn></mrow></msub></mrow></math></span> summation, we show that a specific sequence of well-poised bilateral basic hypergeometric <span><math><mrow><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>ψ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> series form a family of orthogonal functions on the unit circle. We further extract a bilateral matrix inverse from Dougall’s <span><math><mrow><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> summation which we use, in combination with the Pfaff–Saalschütz summation, to derive a summation for a particular bilateral hypergeometric <span><math><mrow><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> series. We finally provide multivariate extensions of the bilateral matrix inverse and the <span><math><mrow><msub><mrow></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> summation in the setting of hypergeometric series associated to the root system <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 6","pages":"Pages 1762-1778"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145374398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}