An isomorphism theorem for Lusztig algebras

Abstract

In [Lu6] Lusztig defined a certain algebra $H,$ which is a direct sum of various algebras $H_{\mathfrak{o}}.$ We establish an explicit algebra isomorphism between each algebra $H_{\mathfrak{o}}$ and some matrix algebra with coefficients in the tensor product of an (affine or finite) Hecke algebra and a group algebra. We give an application.

The results have been contained in G.Lusztig's paper [Lu6] already, and we withdraw this paper. I am very sorry for that!