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Affine Beilinson-Bernstein at the critical level for GL_2

Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019

March 26, 2019 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Sam Raskin (University of Texas, Austin)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

There has long been interest in Beilinson-Bernstein localization for the affine Grassmannian (or affine flag variety). First, Kashiwara-Tanisaki treated the so-called negative level case in the 90's. Some ten years later, Frenkel-Gaitsgory (following work of Feigin-Frenkel and Beilinson-Drinfeld) formulated a conjecture at the critical level and made some progress on it. Their conjecture is more subtle than its negative level counterpart, but also more satisfying. We will review the necessary background from representation theory of Kac-Moody algebras at critical level, formulate the Frenkel-Gaitsgory conjecture, and outline the proof for GL_2.

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