2003/06/24 by Andrew Kresch, Kresch, Andrew, Harry Tamvakis +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #math.AG #msc:05E15 #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/0306337
27 pages, LaTeX, to appear in Journal of Algebraic Geometry
arxiv created 2003/06/24 · arxiv updated 2009/11/30
Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH^*(LG) and show that its multiplicative structure is determined by the ring of (Q^~)-polynomials. We formulate a "quantum Schubert calculus" which includes quantum Pieri and Giambelli formulas, as well as algorithms for computing the structure constants appearing in the quantum product of Schubert classes.