Unipotent Harish-Chandra bimodules

Abstract: Unipotent representations of semisimple Lie groups is a very important and somewhat conjectural class of unitary representations. Some of these representations for complex groups (equivalently, Harish-Chandra bimodules) were defined in the seminal paper of Barbasch and Vogan from 1985 based on ideas of Arthur. From the beginning it was clear that the Barbasch-Vogan construction doesn't cover all unipotent representations. The main construction of this talk is a geometric construction of Harish-Chandra bimodules that should exhaust all unipotent bimodules. A nontrivial result is that all unipotent bimodules in the sense of Barbasch and Vogan are also unipotent in our sense. The proof of this claim is based on the so called symplectic duality that in our case upgrades a classical duality for nilpotent orbits in the version of Barbasch and Vogan. Time permitting I will explain how this works. The talk is based on a joint work with Lucas Mason-Brown and Dmytro Matvieievskyi.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.