English

Quantum cohomology of the Lagrangian Grassmannian

Algebraic Geometry 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0306337,
  title  = {Quantum cohomology of the Lagrangian Grassmannian},
  author = {Andrew Kresch and Harry Tamvakis},
  journal= {arXiv preprint arXiv:math/0306337},
  year   = {2007}
}

Comments

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