Twiseted eigenvarities and self-dual representations

Abstract

For a reductive group G and a finite order Cartan-type automorphism ιof G, we construct an eigenvariety parameterizing ι-invariant cuspidal Hecke eigensystems of G. In particular, for G = Gln, we prove, any self-dual cuspidal Hecke eigensystem can be deformed in a p-adic family of self-dual cuspidal Hecke eigensystems containing a Zariski dense subset of classical points.

55 pages

References in corpus (2)

• Rigidity of p-adic cohomology classes of congruence subgroups of GL(n, Z)
• Cuspidal representations of reductive groups