The boundness of weighted Coxeter groups of rank 3

TL;DR

This paper proves that weighted Coxeter groups of rank 3 are bounded in the sense defined by Lusztig, establishing a key property for this class of algebraic structures.

Contribution

It demonstrates that all weighted Coxeter groups of rank 3 satisfy Lusztig's boundedness condition, a previously unconfirmed property for this class.

Findings

Weighted Coxeter groups of rank 3 are bounded.

The proof confirms Lusztig's boundedness for these groups.

This result advances understanding of Coxeter group properties.

Abstract

We prove that a weighted Coxeter group (W,S,L) is bounded in the sense of G.Lusztig if the rank of W is 3.