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

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