On Exotic Springer Fibres
Neil Saunders (University of Bristol)
Wednesday 3rd December, 2014 16:00-17:00 Maths 516
Let $G$ be a connected reductive algebraic group over the complex numbers, say, and let $W$ be its Weyl group. The Springer Correspondence is a bijection between G-equivariant local systems on the $G$-orbit closures on the nilpotent cone of its Lie algebra, and certain irreducible representations of the Weyl group. Explicitly, the representations come from $W$-actions on the cohomology of the so-called Springer fibres and are somewhat mysterious, as $W$ does not act on every Springer fibre, but does act on the cohomology of every Springer Fibre.
Generally, Springer fibres are difficult to describe geometrically however, their irreducible components often admit nice combinatorial descriptions. In this talk I will give a general exposition on the Springer Correspondence and report on work in progress that seeks to describe the irreducible components of the exotic Springer Fibres in type C.