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

TL;DR

This paper establishes injectivity results connecting Artin groups, Coxeter monoids, and Hecke algebras, revealing new algebraic embeddings and structural insights for right-angled Coxeter and Artin groups.

Contribution

It proves injectivity of Artin groups into Hecke algebra invertible elements and related structures, extending known algebraic embeddings to right-angled cases.

Findings

Artin groups inject into Hecke algebra invertible elements

Coxeter monoid algebra injects into incidence algebra of Bruhat poset

Right-angled Coxeter groups' Hecke algebra injects into Coxeter monoid algebra

Abstract

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 Coxeter monoid algebra and in the one of an incidence algebra).