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

Andrew Mathas


Iwahori-Hecke algebras, Coxeter groups, Kazhdan-Lusztig polynomials.


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


In this paper we investigate the left cell representations of the Iwahori-Hecke algebras associated to a finite Coxeter group W. Let w0 be the element of longest length in W. Our main result shows that Tw0 acts (essentially) as an involution upon the Kazhdan-Lusztig basis 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.

Andrew Mathas
15th May 1996