arXiv - MATH - Representation Theory最新文献_第9页

Local theta correspondences and Langlands parameters for rigid inner twists 刚性内部扭曲的局部θ对应关系和朗兰兹参数

arXiv - MATH - Representation Theory Pub Date : 2024-09-01 DOI: arxiv-2409.00805

Hirotaka Kakuhama

引用次数: 0

Reconstruction of module categories in the infinite and non-rigid settings 无限和非刚性环境中模块类别的重构

arXiv - MATH - Representation Theory Pub Date : 2024-09-01 DOI: arxiv-2409.00793

Mateusz Stroiński, Tony Zorman

{"title":"Reconstruction of module categories in the infinite and non-rigid settings","authors":"Mateusz Stroiński, Tony Zorman","doi":"arxiv-2409.00793","DOIUrl":"https://doi.org/arxiv-2409.00793","url":null,"abstract":"By building on the notions of internal projective and injective objects in a\u0000module category introduced by Douglas, Schommer-Pries, and Snyder, we extend\u0000the reconstruction theory for module categories of Etingof and Ostrik. More\u0000explicitly, instead of algebra objects in finite tensor categories, we consider\u0000quasi-finite coalgebra objects in locally finite tensor categories. Moreover,\u0000we show that module categories over non-rigid monoidal categories can be\u0000reconstructed via lax module monads, which generalize algebra objects. For the\u0000category of finite-dimensional comodules over a (non-Hopf) bialgebra, we give\u0000this result a more concrete form, realizing module categories as categories of\u0000contramodules over Hopf trimodule algebras -- this specializes to our\u0000tensor-categorical results in the Hopf case. Using lax module functors we give\u0000a categorical proof of the variant of the fundamental theorem of Hopf modules\u0000which applies to Hopf trimodules. We also give a characterization of fusion\u0000operators for a Hopf monad as coherence cells for a module functor structure,\u0000using which we similarly reinterpret and reprove the Hopf-monadic fundamental\u0000theorem of Hopf modules due to Brugui`eres, Lack, and Virelizier.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"393 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lifting Brauer indecomposability of a Scott module 提升斯科特模块的布劳尔不可分性

arXiv - MATH - Representation Theory Pub Date : 2024-08-31 DOI: arxiv-2409.00403

Shigeo Koshitani, İpek Tuvay

引用次数: 0

Proof of the Newell-Littlewood saturation conjecture 纽厄尔-利特尔伍德饱和猜想的证明

arXiv - MATH - Representation Theory Pub Date : 2024-08-30 DOI: arxiv-2409.00233

Jaewon Min

引用次数: 0

Some remarks about the faithfulness of the Burau representation of Artin--Tits groups 关于布劳表示法忠实于 Artin-Tits 群的几点评论

arXiv - MATH - Representation Theory Pub Date : 2024-08-30 DOI: arxiv-2409.00144

Asilata Bapat, Hoel Queffelec

引用次数: 0

Irreducible characters of the generalized symmetric group 广义对称群的不可减字符

arXiv - MATH - Representation Theory Pub Date : 2024-08-09 DOI: arxiv-2408.04921

Huimin Gao, Naihuan Jing

引用次数: 0

Koszul duality for generalized steinberg representations of $p$-adic groups p$-adic群的广义斯坦伯格表示的科斯祖尔对偶性

arXiv - MATH - Representation Theory Pub Date : 2024-08-09 DOI: arxiv-2408.05103

Clifton Cunningham, James Steele

引用次数: 0

Polynomial similarity of pairs of matrices 矩阵对的多项式相似性

arXiv - MATH - Representation Theory Pub Date : 2024-08-08 DOI: arxiv-2408.04244

Vitaliy Bondarenko, Anatoliy Petravchuk, Maryna Styopochkina

{"title":"Polynomial similarity of pairs of matrices","authors":"Vitaliy Bondarenko, Anatoliy Petravchuk, Maryna Styopochkina","doi":"arxiv-2408.04244","DOIUrl":"https://doi.org/arxiv-2408.04244","url":null,"abstract":"Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $mathcal{M}(K)$ the\u0000set of all pairs of square matrices of the same size over $K.$ Pairs\u0000$P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $mathcal{M}(K)$ are called similar if\u0000$A_2=X^{-1}A_1X$ and $B_2=X^{-1}B_1X$ for some invertible matrix $X$ over $K$.\u0000Denote by $mathcal{N}(K)$ the subset of $mathcal{M}(K)$, consisting of all\u0000pairs of commuting nilpotent matrices. A pair $P$ will be called {it\u0000polynomially equivalent} to a pair $overline{P}=(overline{A}, overline{B})$\u0000if $overline{A}=f(A,B), overline{B}=g(A ,B)$ for some polynomials $f, gin\u0000K[x,y]$ satisfying the next conditions: $f(0,0)=0, g(0,0)=0$ and $ {rm det}\u0000J(f, g)(0, 0)not =0,$ where $J(f, g)$ is the Jacobi matrix of polynomials\u0000$f(x, y)$ and $g(x, y).$ Further, pairs of matrices $P(A,B)$ and\u0000$widetilde{P}(widetilde{A}, widetilde{B})$ from $mathcal{N}(K)$ will be\u0000called {it polynomially similar} if there exists a pair\u0000$overline{P}(overline{A}, overline{B})$ from $mathcal{N}(K)$ such that $P$,\u0000$overline{P}$ are polynomially equivalent and $overline{P}$, $widetilde{P}$\u0000are similar. The main result of the paper: it is proved that the problem of\u0000classifying pairs of matrices up to polynomial similarity is wild, i.e. it\u0000contains the classical unsolvable problem of classifying pairs of matrices up\u0000to similarity.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Non-noetherian GL-algebras in characteristic two 特征二中的非etherian GL 矩阵

arXiv - MATH - Representation Theory Pub Date : 2024-08-08 DOI: arxiv-2408.04630

Karthik Ganapathy

引用次数: 0

Second adjointness and cuspidal supports at the categorical level 分类层面的第二相邻性和尖顶支持

arXiv - MATH - Representation Theory Pub Date : 2024-08-08 DOI: arxiv-2408.04582

Yuta Takaya

引用次数: 0