Affine Harish-Chandra bimodules and Steinberg-Whittaker localization

Abstract: This talk will be about my paper of the same title with Gurbir Dhillon. It is well-known that the center of the enveloping algebra of an affine Kac-Moody algebra at noncritical level is trivial. Nonetheless, its representation theory shares many features with that of a finite-dimensional semisimple Lie algebra, including a block decomposition of category O. We propose an analogue, for any affine Weyl group orbit at noncritical level, of the category of Kac-Moody representations with the corresponding "generalized central character." We also construct equivalences relating various categories of affine Harish-Chandra bimodules, Whittaker modules, and Whittaker D-modules on the loop group, generalizing known equivalences in the finite-dimensional case proved by Bernstein-Gelfand, Beilinson-Bernstein, Milicic-Soergel, and others.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar