Sangjib Kim
Published 2009-04-25, updated 2010-03-18Version 2
We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.
Comments: 21 pages, v2: title changed, typos and errors corrected
Principal series for general linear groups over finite commutative rings
Modular reduction of the Steinberg lattice of the general linear group
On Unitary Representations of GL2n Distinguished by the Symplectic Group
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