Decomposition for Kazhdan–Lusztig basis elements of the affine Hecke algebra of type [formula omitted

Abstract

With respect to the two-sided cells, we give a decomposition formula for the Kazhdan–Lusztig basis elements of the affine Hecke algebra of type A˜n−1. The main tool is the star operators introduced by Kazhdan and Lusztig. In the appendix, we prove that the left star operator commutes with the right star operator even in the unequal parameter case.