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Algebra Seminar

Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian

Ryan Shifler: Virginia Tech

Location:  Hill 705
Date & time: Wednesday, 22 February 2017 at 2:00PM - 2:11PM

The odd symplectic Grassmannian IG:=IG(k, 2n+1) parametrizes k dimensional subspaces of C2n+1 which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on IG with two orbits, and IG is itself a smooth Schubert variety in the submaximal isotropic Grassmannian IG(k, 2n+2). We use the technique of curve neighborhoods to prove a Chevalley formula in the equivariant quantum cohomology of IG, i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case k=2, and it gives an algorithm to calculate any quantum multiplication in the equivariant quantum cohomology ring.

The current work is joint with L. Mihalcea.

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Department of Mathematics

Department of Mathematics
Rutgers University
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