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Combinatorics, representations and geometry of algebraic supergroups

Connections for Women: Geometric Representation Theory August 28, 2014 - August 29, 2014

August 28, 2014 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Vera Serganova (University of California, Berkeley)
Location: MSRI: Simons Auditorium
Video

Abstract

After brief introduction to algebraic supergroups, we concentrate on the example of the general linear supergroup GL(m|n).

We discuss in detail blocks in the category of finite-dimensional representations of  GL(m|n) and the Kazhdan-Lusztig theory and calculate the multiplicities of standard modules in indecomposable projective modules using categorification approach due to Brundan and weight diagrams of Brundan and Stroppel.

 

Then we talk about flag supermanifolds, Borel-Weil-Bott theory and support variety. If time permits I explain how these geometric methods are used to prove the Kac-Wakimoto conjecture about superdimension of an irreducible representation of GL(m|n).

Supplements
21860?type=thumb Serganova Notes 2.58 MB application/pdf Download
Video/Audio Files

14064

H.264 Video 14064.mp4 336 MB video/mp4 rtsp://videos.msri.org/data/000/021/454/original/14064.mp4 Download
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