Journal of the London Mathematical Society-Second Series最新文献

{"title":"Jordan correspondence and block distribution of characters","authors":"Radha Kessar,&nbsp;Gunter Malle","doi":"10.1112/jlms.70076","DOIUrl":"https://doi.org/10.1112/jlms.70076","url":null,"abstract":"<p>We complete the determination of the <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math> has connected centre. As a consequence, we derive a compatibility between <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>-blocks, <span></span><math>\u0000 <semantics>\u0000 <mi>e</mi>\u0000 <annotation>$e$</annotation>\u0000 </semantics></math>-Harish-Chandra series and Jordan decomposition. Further, we apply our results to complete the proof of Robinson's conjecture on defects of characters.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70076","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A stable splitting for spaces of commuting elements in unitary groups","authors":"Alejandro Adem,&nbsp;José Manuel Gómez,&nbsp;Simon Gritschacher","doi":"10.1112/jlms.70084","DOIUrl":"https://doi.org/10.1112/jlms.70084","url":null,"abstract":"<p>We prove an analogue of Miller's stable splitting of the unitary group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$U(m)$</annotation>\u0000 </semantics></math> for spaces of commuting elements in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$U(m)$</annotation>\u0000 </semantics></math>. After inverting <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>!</mo>\u0000 </mrow>\u0000 <annotation>$m!$</annotation>\u0000 </semantics></math>, the space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>Hom</mo>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mi>U</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{Hom}(mathbb {Z}^n,U(m))$</annotation>\u0000 </semantics></math> splits stably as a wedge of Thom-like spaces of bundles of commuting varieties over certain partial flag manifolds. Using Steenrod operations, we prove that our splitting does not hold integrally. Analogous decompositions for symplectic and orthogonal groups as well as homological results for the one-point compactification of the commuting variety in a Lie algebra are also provided.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143439206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Attainability of the best constant of Hardy–Sobolev inequality with full boundary singularities","authors":"Liming Sun,&nbsp;Lei Wang","doi":"10.1112/jlms.70086","DOIUrl":"https://doi.org/10.1112/jlms.70086","url":null,"abstract":"<p>We consider a type of Hardy–Sobolev inequality, whose weight function is singular on the whole domain boundary. We are concerned with the attainability of the best constant of such inequality. In dimension two, we link the inequality to a conformally invariant one using the conformal radius of the domain. The best constant of such inequality on a smooth bounded domain is achieved if and only if the domain is non-convex. In higher dimensions, the best constant is achieved if the domain has negative mean curvature somewhere. If the mean curvature vanishes but is non-umbilic somewhere, we also establish the attainability for some special cases. In the other direction, we also show that the best constant is not achieved if the domain is sufficiently close to a ball in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$C^2$</annotation>\u0000 </semantics></math> sense.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry and arithmetic of semi-arithmetic Fuchsian groups","authors":"Mikhail Belolipetsky,&nbsp;Gregory Cosac,&nbsp;Cayo Dória,&nbsp;Gisele Teixeira Paula","doi":"10.1112/jlms.70087","DOIUrl":"https://doi.org/10.1112/jlms.70087","url":null,"abstract":"<p>Semi-arithmetic Fuchsian groups is a wide class of discrete groups of isometries of the hyperbolic plane which includes arithmetic Fuchsian groups, hyperbolic triangle groups, groups admitting a modular embedding, and others. We introduce a new geometric invariant of a semi-arithmetic group called stretch. Its definition is based on the notion of the Riemannian center of mass developed by Karcher and collaborators. We show that there exist only finitely many conjugacy classes of semi-arithmetic groups with bounded arithmetic dimension, stretch and coarea. The proof of this result uses the arithmetic Margulis lemma. We also show that when stretch is not bounded there exist infinite sequences of such groups.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gromov–Witten invariants of bielliptic surfaces","authors":"Thomas Blomme","doi":"10.1112/jlms.70081","DOIUrl":"https://doi.org/10.1112/jlms.70081","url":null,"abstract":"<p>Bielliptic surfaces appear as a quotient of a product of two elliptic curves and were classified by Bagnera–Franchis. We give a concrete way of computing their GW-invariants with point insertions using a floor diagram algorithm. Using the latter, we are able to prove the quasi-modularity of their generating series by relating them to generating series of graphs for which we also prove quasi-modularity results. We propose a refinement of these invariants by inserting a <span></span><math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math>-class in the considered GW-invariants.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A stable splitting of factorisation homology of generalised surfaces","authors":"Florian Kranhold","doi":"10.1112/jlms.70089","DOIUrl":"https://doi.org/10.1112/jlms.70089","url":null,"abstract":"&lt;p&gt;For a manifold &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;annotation&gt;$W$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and an &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$smash{E_{smash{d}} }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-algebra &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$A$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the factorisation homology &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∫&lt;/mo&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$smash{int _W A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can be seen as a generalisation of the classical configuration space of labelled particles in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;annotation&gt;$W$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. It carries an action by the diffeomorphism group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Diff&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;&lt;/mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathrm{Diff}{}_partial (W)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and for the generalised surfaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;≔&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;#&lt;/mo&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∖&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;˚&lt;/mo&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70089","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres","authors":"Lukas Bertsch,&nbsp;Ádám Gyenge,&nbsp;Balázs Szendrői","doi":"10.1112/jlms.70074","DOIUrl":"https://doi.org/10.1112/jlms.70074","url":null,"abstract":"<p>We prove a universal substitution formula that compares generating series of Euler characteristics of Nakajima quiver varieties associated with affine ADE diagrams at generic and at certain non-generic stability conditions via a study of collapsing fibres in the associated variation of GIT map, unifying and generalising earlier results of the last two authors with Némethi and of Nakajima. As a special case, we compute generating series of Euler characteristics of non-commutative Quot schemes of Kleinian orbifolds. In type A and rank 1, we give a second, combinatorial proof of our substitution formula, using torus localisation and partition enumeration. This gives a combinatorial model of the fibres of the variation of GIT map, and also leads to relations between our results and the representation theory of the affine and finite Lie algebras in type A.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the real-rootedness of the Eulerian transformation","authors":"Christos A. Athanasiadis","doi":"10.1112/jlms.70083","DOIUrl":"https://doi.org/10.1112/jlms.70083","url":null,"abstract":"<p>The Eulerian transformation is the linear operator on polynomials in one variable with real coefficients that maps the powers of this variable to the corresponding Eulerian polynomials. The derangement transformation is defined similarly. Brändén and Jochemko have conjectured that the Eulerian transforms of a class of polynomials with nonnegative coefficients, which includes those having all their roots in the interval <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$[-1,0]$</annotation>\u0000 </semantics></math>, have only real zeros. This conjecture is proven in this paper. More general transformations are introduced in the combinatorial-geometric context of uniform triangulations of simplicial complexes, where Eulerian and derangement transformations arise in the special case of barycentric subdivision, and are shown to have strong unimodality and gamma-positivity properties. General real-rootedness conjectures for these transformations, which unify various results and conjectures in the literature, are also proposed.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Criteria for extension of commutativity to fractional iterates of holomorphic self-maps in the unit disc","authors":"Manuel D. Contreras,&nbsp;Santiago Díaz-Madrigal,&nbsp;Pavel Gumenyuk","doi":"10.1112/jlms.70077","DOIUrl":"https://doi.org/10.1112/jlms.70077","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a univalent non-elliptic self-map of the unit disc &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(psi _{t})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a continuous one-parameter semigroup of holomorphic functions in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;≠&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;id&lt;/mi&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$psi _{1}ne {sf id}_mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; commutes with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. This assumption does not imply that all elements of the semigroup &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(psi _t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; commute with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we provide a number of sufficient conditions that guarantee that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;∘&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;∘&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${psi _t circ varphi =varphi circ psi _t}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for all &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;se","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Action of \u0000 \u0000 W\u0000 $W$\u0000 -type operators on Schur functions and Schur Q-functions","authors":"Xiaobo Liu,&nbsp;Chenglang Yang","doi":"10.1112/jlms.70080","DOIUrl":"https://doi.org/10.1112/jlms.70080","url":null,"abstract":"<p>In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau-functions of higher KdV hierarchies that satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur Q-functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov–Morozov's formula, which express the Brézin–Gross–Witten and Kontsevich–Witten tau-functions as linear combinations of Q-functions with simple coefficients, respectively.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}