Quantum Pieri rules for isotropic Grassmannians

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology...

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Bibliographic Details
Published in:Inventiones mathematicae 2009-11, Vol.178 (2), p.345-405
Main Authors: Buch, Anders Skovsted, Kresch, Andrew, Tamvakis, Harry
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-009-0201-y