Quantum cohomology of orthogonal Grassmannians

Details Quantum cohomology of orthogonal Grassmannians Quantum cohomology of orthogonal Grassmannians

2003-06-24

arxiv.org/abs/math/0306338v1

Mathematics

Algebraic Geometry

20 pages, LaTeX, to appear in Compositio Mathematica

Scientific paper

Let V be a vector space with a nondegenerate 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 3-point, genus zero Gromov-Witten invariants for OG coincides with that for a corresponding Lagrangian Grassmannian LG, up to an involution.

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