Canonical reduced expression in affine Coxeter groups of type $\tilde{A}_n$, $\tilde{B}_n$, $\tilde{D}_n$
Representation Theory
2025-11-04 v1 Group Theory
Abstract
We classify the elements of by giving a canonical reduced expression for each, using basic tools among which affine length. We give some direct consequences for such a canonical form: a description of left multiplication by a simple reflection, a study of the right descent set, and a proof that the affine length is preserved along the tower of affine Coxeter groups of type , which implies in particular that the corresponding tower of affine Hecke algebras is a faithful tower regardless of the ground ring. We give a similar canonical reduced expression for the elements of and .
Keywords
Cite
@article{arxiv.2511.01702,
title = {Canonical reduced expression in affine Coxeter groups of type $\tilde{A}_n$, $\tilde{B}_n$, $\tilde{D}_n$},
author = {Sadek Al Harbat},
journal= {arXiv preprint arXiv:2511.01702},
year = {2025}
}