On the acceptable elements

Abstract

In this paper, we study the set $B(G,\{\mu \})$ of acceptable elements for any $p$-adic group $G$. We show that $B(G,\{\mu \})$ contains a unique maximal element and the maximal element is represented by an element in the admissible subset of the associated Iwahori-Weyl group.

Final version. 23 pages