In this talk, we will show that every classical self-dual Hecke
eigensystem can be deformed into a p-adic family of classical Hecke
eigensystems. This is a stronger version of the inverse of
Ash-Pollack-Steven's conjecture. To do this, we constructed an
eigenvariety of G_ln parameterizing all self-dual Hecke eigensystems of
Gl_n.