Quantum cohomology of the Lagrangian Grassmannian

Details Quantum cohomology of the Lagrangian Grassmannian Quantum cohomology of the Lagrangian Grassmannian

2003-06-24

arxiv.org/abs/math/0306337v1

Mathematics

Algebraic Geometry

27 pages, LaTeX, to appear in Journal of Algebraic Geometry

Scientific paper

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.

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