Parametrized braid groups of Chevalley groups

Artin groups and Yokonuma-Hecke algebras

We attach to every Coxeter system (W,S) an extension C_W of the corresponding Iwahori-Hecke algebra. We construct a 1-parameter family of (generically surjective) morphisms from the group algebra of the corresponding Artin group onto C_W. When W is finite, we prove that this algebra is a free module of finite rank which is generically semisimple. When W is the Weyl group of a Chevalley group, C_W naturally maps to the associated Yokonuma-Hecke algebra. When W = S_n this algebra can be identified with a diagram algebra called the algebra of `braids and ties'. The image of the usual braid group …

函数域上 Chevalley 群概形的算术子群 I：Bruhat-Tits 建筑关于 $\{P\}$-算术子群的商

Arithmetic subgroups of Chevalley group schemes over function fields I: quotients of the Bruhat-Tits building by $\{P\}$-arithmetic subgroups

本文研究函数域上 Chevalley 群概形的 A-点算术子群在 Bruhat-Tits 建筑上的作用，证明其轨道空间可描述为闭连通 CW-复形与由 Picard 群和群秩参数化的扇形腔室的粘合，并刻画了可嵌入轨道空间的子扇形面。

Elementary equivalence in Artin groups of finite type

Irreducible Artin groups of finite type can be parametrized via their associated Coxeter diagrams into six sporadic examples and four infinite families, each of which is further parametrized by the natural numbers. Within each of these four infinite families, we investigate the relationship between elementary equivalence and isomorphism. For three out of the four families, we show that two groups in the same family are equivalent if and only if they are isomorphic; a positive, but weaker, result is also attained for the fourth family. In particular, we show that two braid groups are elementari…

Subring subgroups in symplectic groups in characteristic 2

In 2012 the second author obtained a description of the lattice of subgroupsof a Chevalley group $G(Φ,A)$, containing the elementary subgroup $E(Φ,K)$ over a subring $K\subseteq A$ provided $Φ=B_n,$ $C_n$ or $F_4$, $n\ge2$, and $2$ is invertible in $K$. It turns out that this lattice splits into a disjoint union of "sandwiches", parametrized by intermediate subrings between $K$ and $A$. In the current article a similar result is proved for $Φ=B_n$ or $C_n$, $n\ge3$, and $2=0$ in $K$. In this settings one has to introduce more sandwiches, namely, the sandwiches are parametrized by form rings $(…