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Steinberg-Whittaker localization and affine Harish--Chandra bimodules
Algebraic Geometry and Number Theory| Speaker: | Gurbir Dhillon, Stanford University |
| Related Webpage: | https://web.stanford.edu/~gsd/ |
| Location: | Zoom |
| 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.
Notes: https://www.math.ucdavis.edu/~egorskiy/AGADM/Dhillon_notes.pdf
Zoom link https://ucdavisdss.zoom.us/j/827266947. Please contact Eugene Gorsky or José Simental Rodríguez for password.