Ting Xue (University of Melbourne)

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.