12:30 p.m., Tuesday (January 16, 2007)
Spherical unitary representations for reductive groups
A classical problem in representation theory, motivated by abstract harmonic analysis
and number theory, is the study of unitary representations of reductive
algebraic groups (for example the general linear, symplectic, or orthogonal groups)
defined over real and p-adic fields.
A unitary representation of a group G is a continuous homomorphism \pi from
G to the group of unitary operators on a complex Hilbert space. One defines the irreducible
unitary representations to be those without proper closed invariant subspaces. Of
particular interest is the identification of the spherical irreducible unitary
representations of G, that is, those which have nontrivial fixed vectors under
the action of a maximal compact subgroup K. The main motivation for their study comes
from the theory of automorphic forms.
In this talk, I will present the background for this problem, and report on joint work
Refreshments will be served at 12:15 p.m. (Math Lounge, MATX 1115).