Quantum cohomology of the Lagrangian Grassmannian

Abstract

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.