Perverse sheaves and the cohomology of regular Hessenberg varieties

Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.

Recording Details

Scientific Areas: 
PIRSA Number: 


Hessenberg varieties are a distinguished family of projective varieties associated to a semisimple complex algebraic group. We use the formalism of perverse sheaves to study their cohomology rings. We give a partial characterization, in terms of the Springer correspondence, of the irreducible representations which appear in the action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. We also prove a support theorem for the universal family of regular Hessenberg varieties, and we deduce that its fibers, though not necessarily smooth, always have the "Kahler package". This is joint work with Peter Crooks.