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.