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Journal of Combinatorial Algebra最新文献

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Cellular subalgebras of the partition algebra 分割代数的单元子代数
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-12-21 DOI: 10.4171/jca/84
Travis Scrimshaw
{"title":"Cellular subalgebras of the partition algebra","authors":"Travis Scrimshaw","doi":"10.4171/jca/84","DOIUrl":"https://doi.org/10.4171/jca/84","url":null,"abstract":"","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"136 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138953348","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}
引用次数: 0
Dimension expanders via quiver representations 通过震颤表示的维度扩展器
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-12-11 DOI: 10.4171/jca/79
Markus Reineke
{"title":"Dimension expanders via quiver representations","authors":"Markus Reineke","doi":"10.4171/jca/79","DOIUrl":"https://doi.org/10.4171/jca/79","url":null,"abstract":"","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"57 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010346","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}
引用次数: 0
New structure on the quantum alcove model with applications to representation theory and Schubert calculus 量子凹形模型的新结构及其在表示理论和舒伯特微积分中的应用
2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-10-31 DOI: 10.4171/jca/77
Takafumi Kouno, Cristian Lenart, Satoshi Naito
{"title":"New structure on the quantum alcove model with applications to representation theory and Schubert calculus","authors":"Takafumi Kouno, Cristian Lenart, Satoshi Naito","doi":"10.4171/jca/77","DOIUrl":"https://doi.org/10.4171/jca/77","url":null,"abstract":"The quantum alcove model associated to a dominant weight plays an important role in many branches of mathematics, such as combinatorial representation theory, the theory of Macdonald polynomials, and Schubert calculus. For a dominant weight, it is proved by Lenart–Lubovsky that the quantum alcove model does not depend on the choice of a reduced alcove path, which is a shortest path of alcoves from the fundamental one to its translation by the given dominant weight. This is established through quantum Yang–Baxter moves, which biject the objects of the models associated to two such alcove paths, and can be viewed as a generalization of jeu de taquin slides to arbitrary root systems. The purpose of this paper is to give a generalization of quantum Yang–Baxter moves to the quantum alcove model corresponding to an arbitrary weight, which was used to express a general Chevalley formula for the equivariant $K$-group of semi-infinite flag manifolds. The generalized quantum Yang–Baxter moves give rise to a “sijection” (bijection between signed sets), and are shown to preserve certain important statistics, including weights and heights. As an application, we prove that the generating function of these statistics does not depend on the choice of a reduced alcove path. Also, we obtain an identity for the graded characters of Demazure submodules of level-zero extremal weight modules over a quantum affine algebra, which can be thought of as a representation-theoretic analogue of the mentioned Chevalley formula.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"22 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765834","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}
引用次数: 3
Annular webs and Levi subalgebras 环状网与李维子代数
2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-10-24 DOI: 10.4171/jca/76
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
{"title":"Annular webs and Levi subalgebras","authors":"Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz","doi":"10.4171/jca/76","DOIUrl":"https://doi.org/10.4171/jca/76","url":null,"abstract":"For any Levi subalgebra of the form $mathfrak{l}=mathfrak{gl}{l{1}}opluscdotsoplusmathfrak{gl}{l{d}}subseteqmathfrak{gl}{n}$ we construct a quotient of the category of annular quantum $mathfrak{gl}{n}$ webs that is equivalent to the category of finite-dimensional representations of quantum $mathfrak{l}$ generated by exterior powers of the vector representation. This can be interpreted as an annular version of skew Howe duality, gives a description of the representation category of $mathfrak{l}$ by additive idempotent completion, and a web version of the generalized blob algebra.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135219719","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}
引用次数: 2
The partial Temperley–Lieb algebra and its representations 部分Temperley-Lieb代数及其表示
2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-10-16 DOI: 10.4171/jca/74
Stephen Doty, Anthony Giaquinto
{"title":"The partial Temperley–Lieb algebra and its representations","authors":"Stephen Doty, Anthony Giaquinto","doi":"10.4171/jca/74","DOIUrl":"https://doi.org/10.4171/jca/74","url":null,"abstract":"In this paper, we give a combinatorial description of a new diagram algebra, the partial Temperley–Lieb algebra, arising as the generic centralizer algebra $mathrm{End}_{mathbf{U}_q(mathfrak{gl}_2)}(V^{otimes k})$, where ${V = V(0) oplus V(1)}$ is the direct sum of the trivial and natural module for the quantized enveloping algebra $mathbf{U}_q(mathfrak{gl}_2)$. It is a proper subalgebra of the Motzkin algebra (the $mathbf{U}_q(fraksl_2)$-centralizer) of Benkart and Halverson. We prove a version of Schur–Weyl duality for the new algebras, and describe their generic representation theory.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079072","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}
引用次数: 4
A uniform characterisation of the varieties of the second row of the Freudenthal–Tits magic square over arbitrary fields 任意域上Freudenthal-Tits幻方第二行变化的统一表征
2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-10-10 DOI: 10.4171/jca/75
Anneleen De Schepper, Jeroen Schillewaert, Hendrik van Maldeghem
{"title":"A uniform characterisation of the varieties of the second row of the Freudenthal–Tits magic square over arbitrary fields","authors":"Anneleen De Schepper, Jeroen Schillewaert, Hendrik van Maldeghem","doi":"10.4171/jca/75","DOIUrl":"https://doi.org/10.4171/jca/75","url":null,"abstract":"We characterise the projective varieties related to the second row of the Freudenthal–Tits magic square, for both the split and the non-split form, using a common, simple and short geometric axiom system. A special case of our result simultaneously captures the analogues over arbitrary fields of the Severi varieties (comprising the $27$-dimensional $mathrm{E_6}$ module and some of its subvarieties), as well as the Veronese representations of projective planes over composition division algebras (most notably the Cayley plane). It is the culmination of almost four decades of work since the original 1984 result by Mazzocca and Melone who characterised the quadric Veronese variety over a finite field of odd order. The latter result is a finite counterpart to the characterisation of the complex quadric Veronese surface by Severi from 1901.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294076","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}
引用次数: 0
The first cotangent cohomology module for matroids 拟阵的第一个余切上同调模
2区 数学
Journal of Combinatorial Algebra Pub Date : 2023-10-06 DOI: 10.4171/jca/73
William Brehm, Alexandru Constantinescu
{"title":"The first cotangent cohomology module for matroids","authors":"William Brehm, Alexandru Constantinescu","doi":"10.4171/jca/73","DOIUrl":"https://doi.org/10.4171/jca/73","url":null,"abstract":"We find a combinatorial formula which computes the first cotangent cohomology module of Stanley–Reisner rings associated to matroids. For arbitrary simplicial complexes we provide upper bounds for the dimensions of the multigraded components of $T^1$. For specific degrees we prove that these bounds are reached if and only if the simplicial complex is a matroid, obtaining thus a new characterization for matroids. Furthermore, the graded first cotangent cohomology turns out to be a complete invariant for nondiscrete matroids.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346116","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}
引用次数: 1
Reflection factorizations and quasi-Coxeter elements 反射分解与拟柯赛特元
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2021-10-27 DOI: 10.4171/jca/70
Patrick Wegener, S. Yahiatene
{"title":"Reflection factorizations and quasi-Coxeter elements","authors":"Patrick Wegener, S. Yahiatene","doi":"10.4171/jca/70","DOIUrl":"https://doi.org/10.4171/jca/70","url":null,"abstract":"We investigate the so-called dual Matsumoto property or Hurwitz action in finite, affine and arbitrary Coxeter groups. In particular, we want to investigate how to reduce reflection factorizations and how two reflection factorizations of the same element are related to each other. We are motivated by the dual approach to Coxeter groups proposed by Bessis and the question whether there is an anlogue of the well known Matsumoto property for reflection factorizations. Our aim is a substantial understanding of the Hurwitz action. We therefore reprove uniformly results of Lewis and Reiner as well as Baumeister, Gobet, Roberts and the first author on the Hurwitz in finite Coxeter groups. Further we show that in an arbitrary Coxeter group all reduced reflection factorizations of the same element appear in the same Hurwitz orbit after a suitable extension by simple reflections. As parabolic quasi-Coxeter elements play an outstanding role in the study of the Hurwitz action, we aim to characterize these elements. We give characterizations of maximal parabolic quasi-Coxeter elements in arbitrary Coxeter groups as well as a characterization of all parabolic quasi-Coxeter elements in affine Coxeter groups.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47626843","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}
引用次数: 3
Computing fusion products of MV cycles using the Mirkovi'c--Vybornov isomorphism 利用Mirkovi c—Vybornov同构计算MV循环的聚变积
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2021-06-13 DOI: 10.4171/JCA/69
R. Bai, Anne Dranowski, J. Kamnitzer
{"title":"Computing fusion products of MV cycles using the Mirkovi'c--Vybornov isomorphism","authors":"R. Bai, Anne Dranowski, J. Kamnitzer","doi":"10.4171/JCA/69","DOIUrl":"https://doi.org/10.4171/JCA/69","url":null,"abstract":"The fusion of two Mirkovic-Vilonen cycles is a degeneration of their product, defined using the Beilinson-Drinfeld Grassmannian. In this paper, we put in place a conceptually elementary approach to computing this product in type $A$. We do so by transferring the problem to a fusion of generalized orbital varieties using the Mirkovic-Vybornov isomorphism. As an application, we explicitly compute all cluster exchange relations in the coordinate ring of the upper-triangular subgroup of $GL_4$, confirming that all the cluster variables are contained in the Mirkovic-Vilonen basis.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45148290","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}
引用次数: 1
Crystals, regularisation and the Mullineux map 水晶，正规化和穆里纳地图
IF 0.9 2区 数学
Journal of Combinatorial Algebra Pub Date : 2021-05-13 DOI: 10.4171/jca/59
M. Fayers
{"title":"Crystals, regularisation and the Mullineux map","authors":"M. Fayers","doi":"10.4171/jca/59","DOIUrl":"https://doi.org/10.4171/jca/59","url":null,"abstract":"The Mullineux map is a combinatorial function on partitions which describes the effect of tensoring a simple module for the symmetric group in characteristic p with the one-dimensional sign representation. It can also be interpreted as an isomorphism between crystal graphs for ŝlp. We give a new combinatorial description of the Mullineux map by expressing this crystal isomorphism as a composition of isomorphisms between different crystals. These isomorphisms are defined in terms of new generalised regularisation maps introduced by Millan Berdasco. We then given two applications of our new realisation of the Mullineux map, by providing purely combinatorial proofs of a conjecture of Lyle relating the Mullineux map with regularisation, and a theorem of Paget describing the Mullineux map in RoCK blocks of symmetric groups.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42911735","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}
引用次数: 1
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