Knuth Relations for the Hyperoctahedral Groups

A character relationship between symmetric group and hyperoctahedral group

We relate character theory of the symmetric groups $S_{2n}$ and $S_{2n+1}$ with that of the hyperoctahedral group $B_n = ({\mathbb Z}/2)^n \rtimes S_n$, as part of the expectation that the character theory of reductive groups with diagram automorphism and their Weyl groups, is related to the character theory of the fixed subgroup of the diagram automorphism.

超八面体 Schur 范畴与超八面体 Web 范畴

Hyperoctahedral Schur Category and Hyperoctahedral Web Category

本文把 Schur 代数与 Web 范畴推广到超八面体群，图解定义超八面体 Web 范畴并证明其与 Schur 范畴等价。

On the Quiver Presentation of the Descent Algebra of the Hyperoctahedral Group

In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of the descent algebra as a homomorphic image of an algebra of binary forests. Here we extend the method to construct a similar presentation of the descent algebra of the hyperoctahedral group, providing a simple proof of the known formula for the quiver of this algebra and a straightforward method for calculating the relations.

Knuth relations, tableaux and MV-cycles

We give a geometric interpretation of the Knuth equivalence relations in terms of the affine Graß mann variety. The Young tableaux are seen as sequences of coweights, called galleries. We show that to any gallery corresponds a Mirković-Vilonen cycle and that two galleries are equivalent if, and only if, their associated MV cycles are equal. Words are naturally identified to some galleries. So, as a corollary, we obtain that two words are Knuth equivalent if, and only if, their associated MV cycles are equal.

偏序集线性扩展上的Bender-Knuth对合

Bender-Knuth involutions on linear extensions of posets

本文研究了偏序集线性扩展上由Bender-Knuth移动生成的置换群的群关系，重点识别满足仙人掌关系及等于线性扩展对称群的偏序集。

Knuth's Coherent Presentations of Plactic Monoids of Type A

We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations amongst the relations. Such extended presentations are used for representations of monoids, in particular, it is a way to describe actions of monoids on categories. Moreover, a coherent presentation provides the first step in the computation of a categorical cofibrant replacement of a monoid. Our construction is based on a rewriting method introduced by Squier t…