Families of representations of Lie groups

Tuesday, October 17, 2017 - 1:00pm
Math 110
Shilin Yu

Beilinson and Bernstein generalized the Borel-Weil-Bott theorem and showed that representations of a (noncompact) reductive Lie group G can be realized as D-modules on flag variety. In this talk, I will show that such D-modules live naturally in families, which explains a mysterious analogy between representation theory of the group G and a related semidirect product group due to Mackey, Higson and Afgoustidis. Connection with Kirillov's coadjoint orbit method will be discussed. The talk is based partially on joint projects with Qijun Tan, Yijun Yao and Conan Leung.