On the left cell representations of Iwahori-Hecke algebras of finite 
Coxeter groups

Andrew Mathas

Keywords

Iwahori-Hecke algebras, Coxeter groups, Kazhdan-Lusztig polyno 

Status

J. London Math. Soc., 54 (1996), 475-488. 

Abstract 

In this paper we investigate the left cell representations of the 
Iwahori-Hecke algebras associated to a finite Coxeter group $W$. Our main 
result shows that $T_{\ws }$, where $\ws $ is the element of longest length 
in $W$, acts essentially as an involution upon the canonical bases of a cell 
representation. We describe some properties of this involution, use it to 
further describe the left cells, and finally show how to realize each cell 
representation as a submodule of $\H$. Our results rely upon certain 
positivity properties of the structure constants of the Kazhdan-Lusztig bases 
of the Hecke algebra and so have not yet been shown to apply to all finite 
Coxeter groups.