SOME GENERIC REPRESENTATIONS, W-GRAPHS, AND DUALITY

[摘要] This paper begins by generalising the notion of a ''W-graph'' to show that the W-graph data determine not one but four closely related representations of the generic Hecke algebra of an arbitrary Coxeter group. Canonical ''Kazhdan-Lusztig bases'' are then constructed for several families of ideals inside the Hecke algebra of a finite Coxeter system (W, S). In particular for each J subset-or-equal-to S we construct the left cell module corresponding to the ''top'' left cell C(J) as a submodule of the Hecke algebra and give a precise description of its canonical basis. In the case of the symmetric group it is shown that every irreducible representation arises as a top cell representation. Finally, analogues of the representations considered are discussed for the case of an infinite Coxeter group. (C) 1994 Academic Press, Inc.

[发布日期] 1994-11-15