Quantum cohomology of orthogonal Grassmannians

Abstract

Let V be a vector space with a non-degenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH ∗ (OG) and show that its product structure is determined by the ring of P˜-polynomials. A 'quantum Schubert calculus' is formulated, which includes quantum Pieri and Giambelli formulas, as well as algorithms for computing Gromov–Witten invariants. As an application, we show that the table of three-point, genus zer Show more