Geordie Williamson
Published 2016-10-20Version 1
These are notes for my Takagi lecture at the University of Tokyo in November, 2016. I survey what is known about simple modules for reductive algebraic groups. The emphasis is on characteristic p>0 and Lusztig's character formula. I explain ideas connecting representations and constructible sheaves (Finkelberg-Mirkovic conjecture) in the spirit of the Kazhdan-Lusztig conjecture. I also discuss a conjecture with S. Riche (a theorem for GL_n) which should eventually make computations more feasible.
Comments: Takagi lecture, November 2016. Preliminary version, comments welcome
An upper bound on the exceptional characteristics for Lusztig's character formula
On a class of double cosets in reductive algebraic groups
Complex representations of reductive algebraic groups with Frobenius maps in the category $\mathscr{X}$
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