On the left cell representations of
of finite Coxeter groups
Keywords Iwahori-Hecke algebras, Coxeter groups,
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.
15th May 1996.