Parahoric fixed spaces in unramified principal series representations

Joshua M. Lansky

Vol. 204 (2002), No. 2, 433–443

DOI: 10.2140/pjm.2002.204.433

Abstract

Let k be a non-archimedean locally compact field and let G be the set of k-points of a connected reductive group defined over k. Let W be the relative Weyl group of G, and let ℋ(G,B) be the Hecke algebra of G with respect to an Iwahori subgroup B of G. We compute the effects of ℋ(G,B) and W on the B-fixed vectors of an unramified principal series representation I of G. We use this computation to determine the dimension of the space of K-fixed vectors in I, where K is a parahoric subgroup of G.

Milestones

Received: 1 August 2000

Revised: 9 January 2001

Published: 1 June 2002