Summary: Distinguished non-Archimedean representations
U. K. Anandavardhanan
Abstract. For a symmetric space (G, H), one is interested in un-
derstanding the vector space of H-invariant linear forms on a rep-
resentation of G. In particular an important question is whether
or not the dimension of this space is bounded by one. We cover
the known results for the pair (G = RE/F GL(n), H = GL(n)), and
then discuss the corresponding SL(n) case. In this paper, we show
that (G = RE/F SL(n), H = SL(n)) is a Gelfand pair when n is
odd. When n is even, the space of H-invariant forms on can have
dimension more than one even when is supercuspidal.
The latter work is joint with Dipendra Prasad.
Let G be a group, and H the group of fixed points of an involution
on G. A representation of G is said to be distinguished with respect
to H, if the space of H-invariant linear forms on is nonzero. More
generally, if the space HomH(, ) is nonzero for a character of H, we
say that is -distinguished with respect to H. In this paper we are
interested in the case when (G, H) is defined over a p-adic field.
The initial impetus for much of the research in this field came from