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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21809

Kresch, A; Tamvakis, H (2004). Quantum cohomology of orthogonal Grassmannians. Compositio Mathematica, 140(2):482-500.

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Abstract

Let V be a vector space with a non-degenerate symmetric form and OG be the
orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give
a presentation for the (small) quantum cohomology ring QH ∗ (OG) and show that
its product structure is determined by the ring of P˜-polynomials. A 'quantum Schubert
calculus' is formulated, which includes quantum Pieri and Giambelli formulas, as well as
algorithms for computing Gromov–Witten invariants. As an application, we show that the
table of three-point, genus zero Gromov–Witten invariants for OG coincides with that for
a corresponding Lagrangian Grassmannian LG, up to an involution.

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20 citations in Web of Science®
17 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
DDC:510 Mathematics
Uncontrolled Keywords:quot schemes; Schubert calculus
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:10 Dec 2013 19:28
Publisher:London Mathematical Society
ISSN:0010-437X
Additional Information:© Foundation Compositio Mathematica 2004.
Publisher DOI:10.1112/S0010437X03000204
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2027200
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1077.14083

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