TWISTED EIGENVARIETIES AND SELF-DUAL REPRESENTATIONS

For a reductive group G and a finite order Cartan-type automorphism iota of G, we construct an eigenvariety parameterizing iota-invariant cuspidal Hecke eigensystems of G. In particular, for G = Gl(n), 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.