Abstract: |
Let G be a semisimple complex Lie group. The set of unipotent representations is a conjectural finite set of unitary representations that should be viewed as a collection of "building blocks" of all unitary representations. In 1985 Barbasch and Vogan defined a set of special unipotent representations, but there are examples of interesting unitary representations not included in this list. In a joint paper with Ivan Losev and Lucas Mason-Brown, we propose a new definition of a set of unipotent representations, which includes all special unipotent representations, and several others such as a metaplectic representation of Sp(2n). In my talk, I will start with a review of special unipotent representations and general expectations of the set of unipotent representations. Then I will explain our definition of a unipotent representation, and show that it meets the aforementioned expectations. In the last part of the talk, I plan to state some natural questions arising from our definition and discuss partial answers to them obtained in an ongoing project with Lucas Mason-Brown and Shilin Yu. |