University of Sydney Algebra Seminar

Anthony Henderson (University of Sydney)

Friday 26th July, 12:05-12:55pm, Carslaw 373

The modular generalized Springer correspondence

Given a connected reductive algebraic group $G$ with Weyl group $W$, the Springer correspondence realizes the category of representations of $W$ as a quotient of the category of $G$-equivariant perverse sheaves on the nilpotent cone. In the original definition, the representations and sheaves were over a field of characteristic zero, but it has recently been shown that the same formalism works with modular coefficients, where the categories are no longer semisimple. In the characteristic-zero case, Lusztig defined a generalized Springer correspondence to interpret the whole category of $G$-equivariant perverse sheaves on the nilpotent cone in terms of representations of relative Weyl groups. We define and determine a modular generalized Springer correspondence in the case $G=\mathrm{GL}(n)$. This is joint work with P. Achar, D. Juteau and S. Riche.