Dirac Cohomology and Unitarity (Unitary Dual Workshop)
Dan Barbasch, Cornell University
Location: Hill 705
Date & time: Thursday, 30 January 2020 at 1:30PM - 2:30PM
The classification of the unitary dual of a real reductive group is a central
problem in the representation theory of such groups. The Dirac operator plays
an important role in singling out an important subset of the unitary dual.
For example, via the index theorem, work of Atiyah and Schmid classify the
discrete series which are essential for the Plancherel formula. Unitary
representations with nontrivial (g,K)-cohomology play an important role in
the theory of automorphic forms. Dirac cohomology (introduced by Vogan) is
another invariant which can be viewed as a generalization of (g,K)-cohomology.
In this talk I will discuss results about a class of representations
which contains the unitary representations with
nontrivial Dirac cohomology. I will emphasize the role of petite and
bottom layer K-types.
This is joint work with Chao-Ping-Dong and Daniel Wong.