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

{"title":"Noncommutative polygonal cluster algebras","authors":"Zachary Greenberg, Dani Kaufman, Merik Niemeyer, Anna Wienhard","doi":"10.1112/jlms.70511","DOIUrl":"https://doi.org/10.1112/jlms.70511","url":null,"abstract":"<p>We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math>-positivity for the groups <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Spin</mi>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Spin}(p,q)$</annotation>\u0000 </semantics></math>. They are generated by mutations of quivers which we call ST-compatible, and which encode the order of the products that appear in the exchange relations. We show that these ST-compatible quivers can be represented by tilings of surfaces by polygons, a generalization of the description of surface type cluster algebras. As examples, we construct tilings which produce ST-compatible versions of the Del Pezzo quivers and the quivers first described by Le for Fock-Goncharov coordinates for Lie groups of type <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>. We show that polygonal cluster algebras have natural evaluations in Clifford algebras, which we use to produce noncommutative generalizations of the Somos sequences and to parameterize the <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math>-positive semigroup of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Spin</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Spin}(2,n)$</annotation>\u0000 </semantics></math>. We indicate how this will be done for the semigroup in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Spin</mi>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Spin}(p,q)$</annotation>\u0000 </semantics></math> and how one will give coordinates for general <span></span><math>\u0000 <semantics>\u0000 <mi>Θ</mi>\u0000 <annotation>$Theta$</annotation>\u0000 </semantics></math>-positive representations into <span></span><math>\u0000 <semantics>\u0000 <mrow","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70511","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147708349","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":"Weighted cycles on weaves","authors":"Daping Weng","doi":"10.1112/jlms.70524","DOIUrl":"https://doi.org/10.1112/jlms.70524","url":null,"abstract":"<p>We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization of this algebra using the skew-symmetric intersection pairing in the simply-laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles to cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster variables.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147708420","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":"Edge-connectivity of graphs with non-negative Bakry–Émery curvature and amply regular graphs","authors":"Kaizhe Chen,&nbsp;Jack H. Koolen,&nbsp;Shiping Liu","doi":"10.1112/jlms.70527","DOIUrl":"https://doi.org/10.1112/jlms.70527","url":null,"abstract":"<p>We establish a sharp edge-connectivity estimate for graphs with non-negative Bakry–Émery curvature. This leads to a geometric criterion for the existence of a perfect matching. Precisely, we show that any regular graph with non-negative Bakry–Émery curvature and an even or infinite number of vertices has a perfect matching. Through a synthesis of combinatorial and curvature-related techniques, we determine the edge-connectivity of (possibly infinite) amply regular graphs.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147708341","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":"L\u0000 p\u0000 \u0000 $L^p$\u0000 -Sobolev inequalities on minimal submanifolds","authors":"Zoltán M. Balogh,&nbsp;Alexandru Kristály,&nbsp;Ágnes Mester","doi":"10.1112/jlms.70521","DOIUrl":"https://doi.org/10.1112/jlms.70521","url":null,"abstract":"<p>The paper is devoted to proving Allard–Michael–Simon-type <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math>-Sobolev inequalities <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p&gt;1)$</annotation>\u0000 </semantics></math> with explicit constants in the setting of Euclidean minimal submanifolds of arbitrary codimension. Our results require separate discussions for the cases <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$pgeqslant 2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$1&lt;p&lt;2$</annotation>\u0000 </semantics></math>, respectively. In particular, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$pgeqslant 2$</annotation>\u0000 </semantics></math>, we obtain an asymptotically sharp and codimension-free Sobolev constant. Our argument is based on the optimal mass transport theory on Euclidean submanifolds and also provides an alternative, unified proof of the recent isoperimetric inequalities of Brendle (J. Amer. Math. Soc., 2021) and Brendle and Eichmair (Notices Amer. Math. Soc., 2024).</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666321","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":"Radon measure-valued solutions of compressible Euler equations and concentration boundary layers in unsteady inviscid flows passing solid obstacles","authors":"Ke Liu,&nbsp;Hairong Yuan","doi":"10.1112/jlms.70520","DOIUrl":"https://doi.org/10.1112/jlms.70520","url":null,"abstract":"<p>For time-dependent compressible Euler flows passing around a fixed solid body in three-dimensional space, there may exist an infinitesimally thin layer of concentrated mass, momentum and energy, wherein all particles impacting the body move along the body's windward boundary surface. By proposing a concept of Radon measure-valued solutions for initial-boundary-value problems of the unsteady compressible Euler equations, which captures both the large-scale three-dimensional distributions of the surrounding flows and the small-scale motions of particles on the two-dimensional boundary surfaces, we derive the governing partial differential equations for the concentration boundary layer—an unsteady (pressureless) compressible Euler system defined on the boundary surface with appropriate source terms. This down-scaling approach can be further generalized to incorporate skin-frictions and phase-transitions within the concentration boundary layer. It constitutes a novel methodology for addressing the complex fluid–solid–heat coupling problems encountered in fluid dynamics. Illustrative examples are presented to demonstrate the applicability of the proposed method to several specific problems, including the derivation for the most general case the Newtonian–Busemann pressure law of hypersonic aerodynamics.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147588647","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":"Skein theory for the Links–Gould polynomial","authors":"Stavros Garoufalidis,&nbsp;Matthew Harper,&nbsp;Rinat Kashaev,&nbsp;Ben-Michael Kohli,&nbsp;Jiebo Song,&nbsp;Guillaume Tahar","doi":"10.1112/jlms.70522","DOIUrl":"https://doi.org/10.1112/jlms.70522","url":null,"abstract":"<p>Building further on work of Marin and Wagner, we give a cubic braid-type skein theory of the Links–Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list of polynomial invariants that can be computed by skein theory. As a consequence, we prove that this skein theory is also shared by the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$V_1$</annotation>\u0000 </semantics></math>-polynomial defined by two of the authors, deducing the equality of the two link polynomials. This implies the specialization properties of the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$V_1$</annotation>\u0000 </semantics></math>-polynomial to the Alexander polynomial and to the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ADO</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <annotation>$mathrm{ADO}_3$</annotation>\u0000 </semantics></math>-invariant, the fact that it is a Vassiliev power series invariant, as well as a Seifert genus bound for knots.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70522","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666322","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":"The second moment of sums of Hecke eigenvalues II","authors":"Ned Carmichael","doi":"10.1112/jlms.70519","DOIUrl":"https://doi.org/10.1112/jlms.70519","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a holomorphic Hecke cusp form of weight &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for &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;SL&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathrm{SL}_2(mathbb {Z})$&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;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&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;annotation&gt;$(lambda _f(n))_{ngeqslant 1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denote its sequence of normalised Hecke eigenvalues. We compute the first and second moments of the sums &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∑&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {S}(x,f)=sum _{xleqslant nleqslant 2x} lambda _f(n)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, on a","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70519","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666320","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":"Arithmetic progressions at the Journal of the LMS","authors":"Ben Green","doi":"10.1112/jlms.70483","DOIUrl":"https://doi.org/10.1112/jlms.70483","url":null,"abstract":"<p>We discuss the papers P. Erdős and P. Turán, <i>On some sequences of integers</i>, J. London Math. Soc. (1) <b>11</b> (1936), 261–264 and K. F. Roth, <i>On certain sets of integers</i>, J. London Math. Soc. (1) <b>28</b> (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70483","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566154","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":"Arithmetic progressions at the Journal of the LMS","authors":"Ben Green","doi":"10.1112/jlms.70483","DOIUrl":"https://doi.org/10.1112/jlms.70483","url":null,"abstract":"<p>We discuss the papers P. Erdős and P. Turán, <i>On some sequences of integers</i>, J. London Math. Soc. (1) <b>11</b> (1936), 261–264 and K. F. Roth, <i>On certain sets of integers</i>, J. London Math. Soc. (1) <b>28</b> (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70483","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565925","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":"147563403","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}