MIT Lie Groups Seminar
Wednesday, February 24, 2021 at 4:30pmVirtual Event
Title : 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.