Informal Friday Seminar: Baine -- Some characters for simple G-modules

Determining the characters of the simple modules for an algebraic group G over an
algebraically closed field of prime characteristic is one of the major open problems in
representation theory.  Recently, Gilmer and Masbaum utilised a TQFT to explicitly
construct a family of simple modules for Sp_2n in all characteristics greater than 3.
In this talk I will explain an algebraic approach to deriving their character formulas,
and show that these weights form part of larger family of weights whose characters are
essentially the same in Types B_n, C_n, and D_n.  Along the way, we shall encounter
sufficient conditions for Lusztig’s conjecture to hold, parity sheaves, and
p-canonical bases.