2003/06/24 by Andrew Kresch, Kresch, Andrew, Harry Tamvakis +1 · 1 citation
Mathematics · #14M15 (Primary) 05E15 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:05E15 #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/0306338
20 pages, LaTeX, to appear in Compositio Mathematica
arxiv created 2003/06/24 · openalex publication_date 2003/06/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.