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

{"title":"Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras","authors":"Chiara Esposito,&nbsp;Andrea Rivezzi,&nbsp;Jonas Schnitzer,&nbsp;Thomas Weber","doi":"10.1112/jlms.70494","DOIUrl":"https://doi.org/10.1112/jlms.70494","url":null,"abstract":"<p>In this paper, we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the nonsymmetric case. The algebraic counterpart of these categories is the notion of a pre-Cartier quasi-bialgebra, which extends the well-known notion of quasi-triangular quasi-bialgebra given by Drinfeld. Our result implies that one can quantize the infinitesimal <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathcal {R}$</annotation>\u0000 </semantics></math>-matrix of any Cartier quasi-bialgebra. We further discuss the emerging concepts of infinitesimal quantum Yang–Baxter equation and Cartier ring, the latter containing braid groups with additional generators that correspond to infinitesimal braidings. Explicit deformations of the representation categories of the gauge-deformed quasi-triangular quasi-bialgebras <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$E(n)$</annotation>\u0000 </semantics></math> are provided.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70494","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563463","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":"Scattering theory for difference equations with operator coefficients","authors":"David Sher,&nbsp;Luis Silva,&nbsp;Boris Vertman,&nbsp;Monika Winklmeier","doi":"10.1112/jlms.70471","DOIUrl":"https://doi.org/10.1112/jlms.70471","url":null,"abstract":"<p>We investigate a class of second-order difference equations featuring operator-valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi-infinite square-summable sequences with entries from a fixed Hilbert space. This work includes a detailed spectral analysis of the perturbed Laplacian and the construction and study of the corresponding objects pertaining to scattering theory, including the entries of the scattering matrix.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70471","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563465","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":"Scattering theory for difference equations with operator coefficients","authors":"David Sher,&nbsp;Luis Silva,&nbsp;Boris Vertman,&nbsp;Monika Winklmeier","doi":"10.1112/jlms.70471","DOIUrl":"https://doi.org/10.1112/jlms.70471","url":null,"abstract":"<p>We investigate a class of second-order difference equations featuring operator-valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi-infinite square-summable sequences with entries from a fixed Hilbert space. This work includes a detailed spectral analysis of the perturbed Laplacian and the construction and study of the corresponding objects pertaining to scattering theory, including the entries of the scattering matrix.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70471","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563308","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":"Fusion systems related to polynomial representations of \u0000 \u0000 \u0000 \u0000 SL\u0000 2\u0000 \u0000 \u0000 (\u0000 q\u0000 )\u0000 \u0000 \u0000 $operatorname{SL}_2(q)$","authors":"Valentina Grazian,&nbsp;Chris Parker,&nbsp;Jason Semeraro,&nbsp;Martin van Beek","doi":"10.1112/jlms.70481","DOIUrl":"https://doi.org/10.1112/jlms.70481","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>q</mi>\u0000 <annotation>$q$</annotation>\u0000 </semantics></math> be a power of a fixed prime <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. We classify up to isomorphism all simple saturated fusion systems on a certain class of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-groups constructed from the polynomial representations of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>SL</mo>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$operatorname{SL}_2(q)$</annotation>\u0000 </semantics></math>, which includes the Sylow <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-subgroups of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>GL</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{GL}_3(q)$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Sp</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{Sp}_4(q)$</annotation>\u0000 </semantics></math> as special cases. The resulting list includes all Clelland–Parker fusion systems, a simple exotic fusion system discovered by Henke–Shpectorov, and a new infinite family of exotic examples.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70481","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563293","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":"Liouville properties for differential inequalities with \u0000 \u0000 \u0000 (\u0000 p\u0000 ,\u0000 q\u0000 )\u0000 \u0000 $(p,q)$\u0000 Laplacian operator","authors":"Mousomi Bhakta,&nbsp;Anup Biswas,&nbsp;Roberta Filippucci","doi":"10.1112/jlms.70490","DOIUrl":"https://doi.org/10.1112/jlms.70490","url":null,"abstract":"<p>In this paper, we establish several Liouville-type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associated with nonnegative solutions to\u0000\u0000 </p><p>In the second part, we consider the inequality\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70490","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563466","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":"Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras","authors":"Chiara Esposito,&nbsp;Andrea Rivezzi,&nbsp;Jonas Schnitzer,&nbsp;Thomas Weber","doi":"10.1112/jlms.70494","DOIUrl":"https://doi.org/10.1112/jlms.70494","url":null,"abstract":"<p>In this paper, we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the nonsymmetric case. The algebraic counterpart of these categories is the notion of a pre-Cartier quasi-bialgebra, which extends the well-known notion of quasi-triangular quasi-bialgebra given by Drinfeld. Our result implies that one can quantize the infinitesimal <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathcal {R}$</annotation>\u0000 </semantics></math>-matrix of any Cartier quasi-bialgebra. We further discuss the emerging concepts of infinitesimal quantum Yang–Baxter equation and Cartier ring, the latter containing braid groups with additional generators that correspond to infinitesimal braidings. Explicit deformations of the representation categories of the gauge-deformed quasi-triangular quasi-bialgebras <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$E(n)$</annotation>\u0000 </semantics></math> are provided.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70494","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563187","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":"Liouville properties for differential inequalities with \u0000 \u0000 \u0000 (\u0000 p\u0000 ,\u0000 q\u0000 )\u0000 \u0000 $(p,q)$\u0000 Laplacian operator","authors":"Mousomi Bhakta,&nbsp;Anup Biswas,&nbsp;Roberta Filippucci","doi":"10.1112/jlms.70490","DOIUrl":"https://doi.org/10.1112/jlms.70490","url":null,"abstract":"<p>In this paper, we establish several Liouville-type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associated with nonnegative solutions to\u0000\u0000 </p><p>In the second part, we consider the inequality\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70490","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563309","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":"Airy wanderer line ensembles","authors":"Evgeni Dimitrov","doi":"10.1112/jlms.70482","DOIUrl":"https://doi.org/10.1112/jlms.70482","url":null,"abstract":"<p>In (J. Stat. Phys. <b>132</b>, 275–290, 2008), Borodin and Péché introduced a generalization of the extended Airy kernel based on two infinite sets of parameters. For an arbitrary choice of parameters, we construct determinantal point processes on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math> for these generalized kernels. In addition, for a subset of the parameter space, we show that the point processes can be lifted to line ensembles on <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathbb {R}$</annotation>\u0000 </semantics></math>, which satisfy the Brownian Gibbs property. Our ensembles generalize the wanderer line ensembles introduced by Corwin and Hammond (Invent. Math. <b>195</b>, 441–508, 2014).</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563055","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":"The fractional Lipschitz caloric capacity of Cantor sets","authors":"Joan Hernández","doi":"10.1112/jlms.70493","DOIUrl":"https://doi.org/10.1112/jlms.70493","url":null,"abstract":"<p>We characterize the <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math>-parabolic Lipschitz caloric capacity of corner-like <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math>-parabolic Cantor sets in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{n+1}$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>s</mi>\u0000 <mo>⩽</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$1/2&lt;sleqslant 1$</annotation>\u0000 </semantics></math>. Despite the spatial gradient of the <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math>-heat kernel lacking temporal antisymmetry, we obtain analogous results to those known for analytic and Riesz capacities.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70493","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562752","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":"When entropy meets Turán: New proofs and hypergraph Turán results","authors":"Ting-Wei Chao,&nbsp;Hung-Hsun Hans Yu","doi":"10.1112/jlms.70473","DOIUrl":"https://doi.org/10.1112/jlms.70473","url":null,"abstract":"<p>In this paper, we provide a new proof of a density version of Turán's theorem. We also rephrase both the theorem and the proof using entropy. With the entropic formulation, we show that some naturally defined entropic quantity is closely connected to other common quantities such as Lagrangian and spectral radius. In addition, we also determine the Turán density for a new family of hypergraphs, which we call tents. Our result can be seen as a new generalization of Mubayi's result on the extended cliques.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562753","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}