Back to Departmental Colloquium: Spring 2007
Departmental Colloquium
Date: Thursday, Jan 25, 2007
Time: 4:15PM
Location: JWB 335
Dan Ciubotaru
MIT
Title |
Spherical unitary representations. |
Abstract |
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 π 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 attempt to present the background for this problem, and report on joint work with D. Barbasch on the identification of spherical unitary representations. |
Number Theory
Representation Theory