Matching theorems for twisted orbital integrals

Rebecca A. Herb

Vol. 171 (1995), No. 2, 409–428

DOI: 10.2140/pjm.1995.171.409

Abstract

Let F be a ρ-adic field and E a cyclic extension of F of degree d corresponding to the character κ of F^×. For any positive integer m, we consider H = GL(m,E) as a subgroup of G = GL(md,F). In this paper we discuss matching of orbital integrals between H and G. Specifically, ordinary orbital integrals corresponding to regular semisimple elements of H are matched with orbital integrals on G which are twisted by the character κ. For the general situation we only match functions which are smooth and compactly supported on the regular set. If the extension E∕F is unramified, we are able to match arbitrary smooth, compactly supported functions.

Mathematical Subject Classification 2000

Primary: 22E50

Secondary: 22E35

Milestones

Received: 29 June 1993

Published: 1 December 1995