Stephen Donkin
It is shown that the endomorphism algebra of an arbitrary Young permutation module is cellular. Those are are quasi-hereditary are then determined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Cellularity of endomorphism algebras of tilting objects
研究显示，最高权范畴中倾斜对象的结束同态代数本质上是可数代数，并通过构造标准基推广了相关理论。
We exhibit for all positive integers r, an explicit cellular structure for the endomorphism algebra of the r'th tensor power of an integral form of the Weyl module with highest weight d of the quantised enveloping algebra of sl2. When q is specialised to a root of unity of order bigger than d, we consider the corresponding specialisation of the tensor power. We prove one general result which gives sufficient conditions for the commutativity of specialisation with the taking of endomorphism algebras, and another which relates the multiplicities of indecomposable summands to the dimensions of si…
Given $r \in \mathbf{N},$ let $λ$ be a partition of $r$ with at most two parts. Let $\mathbf{F}$ be a field of characteristic 3. Write $M^λ$ for the $\mathbf{F}S_r$-permutation module corresponding to the action of the symmetric group $S_r$ on the cosets of the maximal Young subgroup $S_λ.$ We construct a full set of central primitive idempotents in $\text{End}_{\mathbf{F} S_r}(M^λ)$ in this case. We also determine the Young module corresponding to each primitive idempotent that we construct.
Let $K$ be a field of characteristic two, and let $λ$ be a two-part partition of some natural number $r$. Denote the permutation module corresponding to the (maximal) Young subgroup $Σ_λ$ in $Σ_r$ by $M^λ$. We construct a full set of orthogonal primitive idempotents of the centraliser subalgebra $S_K(λ) = 1_λS_K(2,r) 1_λ= End_{KΣ_r}(M^λ)$ of the Schur algebra $S_K(2,r)$. These idempotents are naturally in one-to-one correspondence with the 2-Kostka numbers.
Let $Σ_r$ be the symmetric group acting on $r$ letters, $K$ be a field of characteristic 2 and $λ$ and $μ$ be partitions of $r$ in at most two parts. Denote the permutation module corresponding to the Young subgroup $Σ_λ$ in $Σ_r$ by $M^λ$, and the indecomposable Young module by $Y^μ$. We give an explicit presentation of the endomorphism algebra ${\rm End}_{K[Σ_r]}(Y^μ)$, using the idempotents found by Doty, Erdmann and Henke in [1].
We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Brou{é} correspondence. We then prove new reduction theorems for the signed $p$-Kostka numbers, defined to be the multiplicities of signed Young modules as direct summands of signed Young permutation modules. We end by classifying the indecomposable signed Young permutation modules and determining their endomorphism algebras.
The source permutation module of a block of a finite group algebra
本文引入有限群代数块分量的源置换模，证明其在 splendid Morita 等价下不变，并将 Sylow 置换模自内射性与 Alperin 权猜想的相关结果推广到该模，同时计算了若干具体情形。
A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined, which are some cyclotomic quotients of affine walled Brauer algebras. We establish a super Schur-Weyl duality between affine walled Brauer algebras and general linear Lie superalgebras, and realize level two walled Brauer algebras as endomorphism algebras of tensor modules of Kac modules with mixed tensor products of the natural module and its dual over general …
The (Iwahori-)Hecke algebra in the title is a $q$-deformation $\sH$ of the group algebra of a finite Weyl group $W$. The algebra $\sH$ has a natural enlargement to an endomorphism algebra $\sA=\End_\sH(\sT)$ where $\sT$ is a $q$-permutation module. In type $A_n$ (i.e., $W\cong {\mathfrak S}_{n+1}$), the algebra $\sA$ is a $q$-Schur algebra which is quasi-hereditary and plays an important role in the modular representation of the finite groups of Lie type. In other types, $\sA$ is not always quasi-hereditary, but the authors conjectured 20 year ago that $\sT$ can be enlarged to an $\sH$-module …
This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of permutation characters of finite general linear groups. In particular, complete sets of inequivalent, irreducible modules for semisimple specializations of these algebras are constructed.
We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra of gl_n (or sl_n). The endomorphism algebras and the generic algebras are cellular. We give several equivalent descriptions of these algebras, find a number of explicit bases, and describe indexing sets for their irreducible representations.
The geometry of permutation modules
本文利用Brauer商对正特征下有限群置换模的导出范畴进行分层，并通过约化到初等阿贝尔群及扭曲上同调描述紧对象谱，最终给出thick理想与localizing理想的分类。
Diagrammatic Okada monoid and cellularity of the Okada algebra
本文利用带标记非交叉弧图实现Okada代数与Okada幺半群，证明其维数、正则性等性质，构造其胞腔基并提出相关猜想，推进对称群与Okada代数的类比研究。
Permutation groups and symmetric Hecke algebras
本文研究置换群与海肯代数的对称性，提出p-S置换群和S置换群的概念，并扩展了先前关于海肯代数对称性的研究。
In this paper, we define the Yokonuma-Schur algebra $\text{YS}_{q}(r,n)$ as the endomorphism algebra of a permutation module for the Yokonuma-Hecke algebra $\text{Y}_{r,n}(q).$ We prove that $\text{YS}_{q}(r,n)$ is cellular by constructing an explicit cellular basis following the approach in [DJM], and we further show that it is a quasi-hereditary cover of $\text{Y}_{r,n}(q)$ in the sense of Rouquier following [HM2]. We also introduce the tilting modules for $\text{YS}_{q}(r,n).$ In the appendix, we define and study the cyclotomic Yokonuma-Schur algebra in a similar way.
Quasi-cellular categories and the structure of the Brauer category
本文提出拟细胞范畴概念，研究 Brauer 范畴的拟细胞结构，构造到矩阵 Brauer 范畴的线性函子，证明非奇异参数下该函子为同构且 Brauer 范畴与置换子范畴 Morita 等价，推广了 Brauer 代数的相关结果。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。