On Dirac cohomology of complex classical Lie groups


主讲人:Daniel Kayue Wong,香港中文大学(深圳)助理教授




内容介绍:Let $G$ be a real reductive Lie group, and $\hat{G}^d$ be the collection of ?irreducible unitary representations with nonzero Dirac cohomology. In the ?special case when $G$ is a complex group (treated as a real group), Barbasch and ?Pandzic conjectured $\hat{G}^d$ can be obtained from parabolic induction on some ?unipotent representations. On the other hand, Dong reduced the study of ?$\hat{G}^d$ to a finite set of representations called scattered representations. ?In this talk, we will see how these two approaches of $\hat{G}^d$ can be ?reconciled for complex classical Lie groups, which in turn will verify a couple ?of conjectures of Barbasch-Pandzic, and identify the scattered representations ?computed by Dong using the atlas program. This is a joint work with Dan Barbasch ?and Chao-ping Dong.