On the Steinberg character of a semisimple p-adic group

Ju-Lee Kim and George Lusztig

Vol. 265 (2013), No. 2, 499–509

DOI: 10.2140/pjm.2013.265.499

Abstract

We show that the character of the Steinberg representation of a split semisimple p-adic group at a very regular element is given (up to sign) by a power of q, the number of elements in the residue field. We also show that (under an assumption on the characteristic) the character of an Iwahori-spherical representation at a split very regular element is given by a trace in the corresponding Hecke algebra module.

Keywords

p-adic group, character, unipotent representation

Mathematical Subject Classification 2010

Primary: 20G99

Milestones

Received: 2 August 2012

Revised: 26 November 2012

Accepted: 28 November 2012

Published: 28 August 2013