Equivariant quantum cohomology of the odd symplectic Grassmannian

摘要

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 multiplication in the equivariant quantum cohomology ring.