Anthony Henderson (University of Sydney)

Friday 24th August, 12.05-12.55pm, Carslaw 373

Orbit closures in the enhanced nilpotent cone

It is well known that GL_n(C)-orbits in the nilpotent cone N (consisting of n×n nilpotent complex matrices) are parametrized by partitions of n. Some of the geometry of the orbit closures is reflected in their intersection cohomology polynomials, which were shown by Lusztig to equal the combinatorial Kostka-Foulkes polynomials. The `enhanced nilpotent cone' of the title is nothing but the product Cⁿ×N (consisting of pairs of a vector and a nilpotent matrix). The obvious action of GL_n(C) still has finitely many orbits, now parametrized by bipartitions of n. I will discuss the closures of these orbits, and a conjecture on their intersection cohomology polynomials.

This is joint work with Pramod Achar (Louisiana State University).