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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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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||quot schemes; Schubert calculus|
|Deposited On:||29 Nov 2010 16:26|
|Last Modified:||10 Dec 2013 19:28|
|Publisher:||London Mathematical Society|
|Additional Information:||© Foundation Compositio Mathematica 2004.|
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