On Dirac cohomology of complex classical Lie groups


主講人:Daniel Kayue Wong,香港中文大學(深圳)助理教授




內容介紹: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.