Title

Orbit closures in the enhanced nilpotent cone

Document Type

Article

Publication Date

9-10-2008

Abstract

We study the orbits of G = GL (V) in the enhanced nilpotent cone V × N, where N is the variety of nilpotent endomorphisms of V. These orbits are parametrized by bipartitions of n = dim V, and we prove that the closure ordering corresponds to a natural partial order on bipartitions. Moreover, we prove that the local intersection cohomology of the orbit closures is given by certain bipartition analogues of Kostka polynomials, defined by Shoji. Finally, we make a connection with Kato's exotic nilpotent cone in type C, proving that the closure ordering is the same, and conjecturing that the intersection cohomology is the same but with degrees doubled. © 2008 Elsevier Inc. All rights reserved.

Publication Source (Journal or Book title)

Advances in Mathematics

First Page

27

Last Page

62

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