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Postnikov, Alexander

Affine approach to quantum Schubert calculus. (English) Zbl 1081.14070

Duke Math. J. 128, No. 3, 473-509 (2005).
In this article, the author presents a quantum cohomology analogue of skew Schur polynomials. These are certain symmetric polynomials labeled by shapes that are embedded in a torus. The author shows that the Gromov-Witten invariants are the expansion coefficients of these toric Schur polynomials in the basis of the ordinary Schur polynomials. The toric Schur polynomials are defined as sums over certain cylindrical semistandard tableaux. This paper makes an important contribution to the quantum cohomology theory of the Grassmannians.
Reviewer: V. Lakshmibai (Boston)

Cited in 5 Reviews
Cited in 52 Documents

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)

Keywords:

quantum cohomology; Schur polynomials; Gronov-Witten invariants
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Full Text: DOI arXiv Euclid

References:

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