Seminars & Colloquia Calendar
The defining equations for some nilpotent varieties
Eric Sommers, University of Massachusetts
Location: Hill 705
Date & time: Friday, 05 October 2018 at 12:00PM - 1:00PM
Abstract: In his 1963 paper "Lie group representations on polynomial rings," Kostant found the defining equations for the nilpotent cone of a simple Lie algebra and also proved it is a normal variety. Later Broer showed uniformly that the closure of the next biggest nilpotent orbit, the subregular nilpotent orbit, is a normal variety and found its defining equations. We generalize Broer's technique to the class of nilpotent orbits that are Richardson orbits for orthogonal short simple roots. The proof involves cohomological results for line bundles on cotangent bundles of generalized flag varieties and a result related to flat bases of invariant polynomials.
This is joint work with Ben Johnson.