The cohomology of a regular semisimple Hessenberg variety carries a representation of the Weyl group, defined by Tymoczko. At one extreme is the regular representation (concentrated in degree 0); at the other, the trivial W-action on the cohomology of the flag variety. This representation can be reinterpreted in terms of the geometry of nilpotent Hessenberg varieties, which we discuss in this talk. Based on joint work with Martha Precup.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Various Guises of Reflection Arrangements.