Upcoming Seminars

Let G be a reductive group over a local field, and H be a spherical subgroup. An irreducible representation of G is said to be distinguished by H if it has an H-invariant continuous linear functional. The study of distinguished representations is of much current interest, because of their relation to the Plancherel measure on G/H and to periods of automorphic forms.

While a complete classification seems to be out of reach, in a joint work with E. Sayag we established simple geometric necessary conditions for distinction. The conditions are formulated in terms of the nilpotent orbit associated to the representation. In the talk I will focus on the case of real reductive G, based on the recent preprint arXiv:2001.11746. Our main tool is the theory of associated varieties of modules over the Lie algebra of G.