Vol. 95, No. 1, 1981

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Base change lifting and Galois invariance

Joe Repka

Vol. 95 (1981), No. 1, 205–212

Let G be a quasi-split connected reductive group defined over the reals. Every irreducible representation π of GR has a base change lifting Π, a representation of GC, such that Π is equivalent to its conjugate Πσ. We prove that if G = GL(n), every Π which is equivalent to Πσ 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
Received: 29 February 1980
Published: 1 July 1981
Joe Repka