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Quantum cohomology of the Lagrangian Grassmannian


Kresch, A; Tamvakis, H (2003). Quantum cohomology of the Lagrangian Grassmannian. Journal of Algebraic Geometry, 12(4):777-810.

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.

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.

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32 citations in Web of Science®
34 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2003
Deposited On:29 Nov 2010 16:26
Last Modified:17 Dec 2017 06:24
Publisher:University Press, Inc.
ISSN:1056-3911
Publisher DOI:https://doi.org/10.1090/S1056-3911-03-00347-3
Official URL:http://www.ams.org/journals/jag/2003-12-04/S1056-3911-03-00347-3
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1051.53070
http://www.ams.org/mathscinet-getitem?mr=1993764

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