SMS scnews item created by Anthony Henderson at Sun 19 Aug 2007 1656
Type: Seminar
Distribution: World
Expiry: 24 Aug 2007
Calendar1: 24 Aug 2007 1205-1255
CalLoc1: Carslaw 373
CalTitle1: Algebra Seminar: Henderson -- Orbit closures in the enhanced nilpotent cone
Auth: anthonyh@asti.maths.usyd.edu.au

Algebra Seminar

Orbit closures in the enhanced nilpotent cone

Anthony Henderson

24th August, 12:05-12:55pm, Carslaw 373


Abstract

It is well known that GLn(C)-orbits in the nilpotent cone N (consisting of nn 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 CnN (consisting of pairs of a vector and a nilpotent matrix). The obvious action of GLn(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).


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