# 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.