Base change lifting and Galois invariance

Joe Repka

Vol. 95 (1981), No. 1, 205–212

DOI: 10.2140/pjm.1981.95.205

Abstract

Let G be a quasi-split connected reductive group defined over the reals. Every irreducible representation π of G_R has a base change lifting Π, a representation of G_C, such that Π is equivalent to its conjugate Π^σ. We prove that if G = GL(n), every Π which is equivalent to Π^σ is the lifting of some π, but show by examples that this is not always true for general G. Finally we discuss the analogous global question and show that there are global cusp forms on PGL(2) which are Galois invariant but not liftings.

Mathematical Subject Classification 2000

Primary: 22E47

Secondary: 22E55

Milestones

Received: 29 February 1980

Published: 1 July 1981