Combinatorics, representations and geometry of algebraic supergroups
Connections for Women: Geometric Representation Theory August 28, 2014 - August 29, 2014
Location: MSRI: Simons Auditorium
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).
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