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Tilting modules for reductive groups and the Hecke category, II

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Geordie Williamson
C. Stroppel
University of Sydney
Tue, 2018-01-30 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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