On the local constancy of characters

Abstract

The character of an irreducible admissible representation of a $p$-adic reductive group is known to be a constant function in some neighborhood of any regular semisimple element $\gamma$ in the group. Under certain mild restrictions on $\gamma$, we give an explicit description of a neighborhood of $\gamma$ on which the character is constant.

13 pages, corrected typos, minor changes to content