Algebra Seminar: Xue -- The Springer correspondence for symmetric spaces and Hessenberg varieties

Ting Xue (University of Melbourne) 

Wednesday September 7, 12-1pm, Place: Carslaw 375 

The Springer correspondence for symmetric spaces and Hessenberg varieties 

The Springer correspondence relates nilpotent orbits in the Lie group of a reductive
algebraic group to irreducible representations of the Weyl group.  We develop a Springer
theory in the case of symmetric spaces using Fourier transform, which relates nilpotent
orbits in this setting to irreducible representations of Hecke algebras at q=-1.  We
discuss applications in computing cohomology of Hessenberg varieties.  Examples of such
varieties include classical objects in algebraic geometry: Jacobians, Fano varieties of
k-planes in the intersection of two quadrics, etc.  This is joint work with Tsao-hsien
Chen and Kari Vilonen.