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Steinberg-Whittaker localization and affine Harish--Chandra bimodules

Algebraic Geometry

Speaker: Gurbir Dhillon, Stanford University
Related Webpage: https://web.stanford.edu/~gsd/
Location: Zoom (Online)
Start time: Wed, May 27 2020, 1:10PM

A fundamental result in representation theory is Beilinson--Bernstein localization, which identifies the representations of a reductive Lie algebra with fixed central character with D-modules on (partial) flag varieties. We will discuss a localization theorem which identifies the same representations instead with (partial) Whittaker D-modules on the group. In this perspective, representations with a fixed central character are equivalent to the parabolic induction of a `Steinberg' category of D-modules for a Levi.

Time permitting, we will explain how these methods can be used to identify a subcategory of Harish--Chandra bimodules for an affine Lie algebra and prove that it behaves analogously to Harish--Chandra bimodules with fixed central characters for a reductive Lie algebra. In particular, it contains candidate principal series representations for loop groups. This a report on work with Justin Campbell.

Zoom link https://ucdavisdss.zoom.us/j/827266947. Please contact Eugene Gorsky or José Simental Rodríguez for password.