Cells and representations of right-angled Coxeter groups

Artin group injection in the Hecke algebra for right-angled groups

We prove some injectivity results: that a Coxeter monoid $\mathbb{Z}$-algebra (or $0$-Hecke algebra) injects in the incidence $\mathbb{Z}$-algebra of the corresponding Bruhat poset, for any Coxeter group; that the Hecke algebra of a right-angled Coxeter group injects in the Coxeter monoid $\mathbb{Z}[q,q^{-1}]$-algebra (and then in the incidence $\mathbb{Z}[q,q^{-1}]$-algebra of the corresponding Bruhat poset); that a right-angled Artin group injects in the group of invertible elements of the Hecke algebra of the corresponding Coxeter group (and then in the group of invertible elements of a Co…

关于右角Coxeter群下中心列的连续因子

On consecutive factors of the lower central series of right-angled Coxeter groups

该研究针对右角Coxeter群的下中心列及相伴分次Lie代数展开，核心是描述任意$\u212c$对应的第四分次分量的基，为相关代数结构分析提供基础。

Presentation of right-angled Soergel categories by generators and relations

Soergel bimodule category B is a categorification of the Hecke algebra of a Coxeter system (W,S). We find a presentation of B (as a tensor category) by generators and relations when W is a right-angled Coxeter group.

Conjectures P1-P15 for Coxeter groups with complete graph

We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using deceasing induction on $ \mathbf{a} $-values and a kind of decomposition formula of Kazhdan-Lusztig basis elements. As a byproduct, we give a description of the left, right, and two-sided cells. In the appendix, we prove P1-P15 for right-angled Coxeter groups by the same methods.

标记多着色、部分交换李超代数与直角 Coxeter 群

Marked multi-colorings, partially commutative Lie superalgebras and right-angled Coxeter groups

本文利用标记多着色及相关多项式，通过分母恒等式研究 BKM 超代数根重数，并引入 PCLSAs，建立其与直角 Coxeter 群的联系及 Hilbert 级数公式。

Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings

We obtain a complete characterisation of factorial multiparameter Hecke von Neumann algebras associated with right-angled Coxeter groups. Considering their $\ell^p$-convolution algebra analogues, we exhibit an interesting parameter dependence, contrasting phenomena observed earlier for group Banach algebras. Translated to Iwahori-Hecke von Neumann algebras, these results allow us to draw conclusions on spherical representation theory of groups acting on right-angled buildings, which are in strong contrast to behaviour of spherical representations in the affine case. We also investigate certain…