Kazhdan-Lusztig basis, Wedderburn decomposition, and Lusztig's homomorphism for Iwahori-Hecke algebras

摘要

Let (W, S) be a finite Coxeter system and A := Z[Gamma] be the group algebra of a finitely generated free abelian group Gamma. Let H be an Iwahori-Hecke algebra of (W, S) over A with parameters v(s). Further let K be an extension field of the field of fractions of A and KJf be the extension of scalars. In this situation Kazhdan and Lusztig have defined their famous basis and the so-called left cell modules.