Orbit closures in the enhanced nilpotent cone
By Pramod N. Achar, Anthony Henderson. 2007
93 citations recorded by the source corpus.
We study the orbits of G=GL(V) in the enhanced nilpotent cone , where is the variety of nilpotent endomorphisms of V. These orbits are parametrized by bipartitions of n=dimV, 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
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d3d11d1221c00e44c3be4a2a5de35ff5e36f7ffa
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- An exotic Deligne-Langlands correspondence for symplectic groups (2006, methodology): “OC for a closed subvariety C⊂Ea X to ch[OC] = [C] + lower degree terms ∈H2dimC(Ea X) ⊕···⊕H0(E a X). 2) The first part of Theorem 6.2 is valid even for integral coefficient case when G(s) ⊂GL(n,C) (c.f. [AH08])2. Here we present a proof along the line of earlier versions of this paper, with an enhancem”
- Mirabolic affine Grassmannian and character sheaves (2008, unknown): “Hence the Frobenius action on the IC stalks of ( N × V ) ( λ,µ ) is encoded in the polynomials Π ( λ ′ ,µ ′ ) , ( λ,µ ) introduced after Proposition 14.”