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Tilting modules for reductive groups and the Hecke category, IV

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Geordie Williamson
University of Sydney
Tue, 2018-02-13 16:15 - 18:15
MPIM Lecture Hall

Determining the characters of indecomposable tilting modules for reductive groups is one of the most fundamental
open problems in modular representation theory. A solution for GL_n would answer the question of the dimensions of
the simple modules for the symmetric group in characteristic p. It is related to (but almost certainly harder than) the
determination of the simple characters. I will  describe a new algorithm (based on a long and ongoing series of work
with Elias, Riche, Libedinsky, Achar-Makisumi-Riche) which allows one to calculate much further. There are many
ideas involved, including from geometric representation theory and the representation theory of monoidal categories.
Long calculations using this algorithm on a super computer at the MPI led Lusztig and I to a conjecture for SL_3
which I find quite startling, and I hope to explain in detail. If time permits I will also discuss Sp_4 (joint work in
progress with Jensen and Lusztig), which looks even more interesting!

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