Dolbeault-Dirac operators on complex homogeneous spaces
Speaker: Yanli Song, University of Toronto
Abstract: Let G be a connected semisimple Lie group with a compact Cartan subgroup H. As was conjectured by Langlands and solved by Schmid, the L^2-cohomology spaces of homogeneous, holomorphic line bundles over the manifold G/H vanishes for all but one degree, and the only non-vanishing degree gives a G-representation of the discrete series. In this talk, I will discuss an analytic approach to the above ''vanishing" result. It will lead to a geometric computation of the K-multiplicities of the discrete series representations. This is a work in progress.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm