## Geometry and Physics Seminar: Jim Carrell

- Date: 03/03/2014
- Time: 15:00

University of British Columbia

Surjectivity and lifting the Weyl group action to the equivariant cohomology of a Springer fibre.

A famous result of Springer says that the Weyl group of a reductive algebraic group G (over C) acts on the cohomology of the subvariety X_u of the flag variety G/B consisting of the flags fixed by a unipotent u in G. This result was unexpected since W does not act on X_u itself. Recently, Kumar - Procesi and Goresky - MacPherson showed that Springer's action lifts to the equivariant cohomology of X_u with respect to the maximal torus in C_G(u) for so called parabolic unipotents u with the proviso that the cohomology morphism j*: H*(G/B) \to H*(X_u) is surjective. In this talk we will describe the parabolic unipotents for which j* is surjective and indicate a direct proof of lifting.

This is a live e-seminar hosted by PIMS-UBC in ESB 4127 and broadcast to The University of Alberta in CAB 449