Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian

2017/06/01 by Mihalcea, Leonardo C., Shifler, Ryan M.
#14M15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 14N35 #Secondary 14N15

paper · doi:10.48550/arxiv.1706.00385

Abstract

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.

Related

• Equivariant quantum cohomology of homogeneous spaces
• Quantum Giambelli formulas for isotropic Grassmannians
• Curve neighborhoods of Schubert Varieties in the odd symplectic Grassmannian
• Quantum cohomology of the Lagrangian Grassmannian
• Quantum cohomology of the odd symplectic Grassmannian of lines