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    Geometric Methods in Representation Theory Seminar

    Steven Sam, UC Berkeley

    • Geometric Methods in Representation Theory Seminar
    When Mar 08, 2013
    from 04:00 PM to 05:00 PM
    Where Phillips Hall 367
    Contact Name
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    Title: Homology of Littlewood complexes

    Abstract: The universal character ring of Koike-Terada allows one to calculate with the character theory of "infinite rank" classical groups similar to how one uses the ring of symmetric functions in infinitely many variables to calculate with the character theory of the infinite general linear group. For this to be useful, one needs a specialization map to usual character rings. This has the strange property that an irreducible character specializes either to 0 or plus or minus an irreducible character. We explain this by showing that this is the combinatorial shadow of the behavior of the derived functors of a left exact functor from a category of representations of an infinite rank classical group to the category of representations of a finite rank classical group. The calculation of these derived functors uses the Borel-Weil-Bott theorem in a non-direct way and connects to some classical invariant theory. I will explain some examples and how these different ingredients are connected. This is based on joint work with Andrew Snowden and Jerzy Weyman.