Affine approach to quantum Schubert calculus
| dc.creator | Postnikov, Alexander | |
| dc.date | 2002-05-15 | |
| dc.date | 2002-06-19 | |
| dc.date.accessioned | 2026-07-07T04:48:31Z | |
| dc.date.available | 2026-07-07T04:48:31Z | |
| dc.description | This article presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we show that the coefficients in the expansion of these toric Schur polynomials, in terms of the regular Schur polynomials, are exactly the 3-point Gromov-Witten invariants; which are the structure constants of the quantum cohomology ring. This construction implies that the Gromov-Witten invariants of the Grassmannian are invariant with respect to the action of a twisted product of the groups S_3, (Z/nZ)^2, and Z/2Z. The last group gives a certain strange duality of the quantum cohomologythat inverts the quantum parameter q. Our construction gives a solution to a problem posed by Fulton and Woodward about the characterization of the powers of the quantum parameter q that occur with nonzero coefficients in the quantum product of two Schubert classes. The strange duality switches the smallest such power of q with the highest power. We also discuss the affine nil-Temperley-Lieb algebra that gives a model for the quantum cohomology. | |
| dc.description | amsart LaTeX, 33 pages, 7 colored figures; v2: minor corrections, references added | |
| dc.identifier | https://arxiv.org/abs/math/0205165 | |
| dc.identifier | http://arxiv.org/abs/math/0205165 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64075 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 05E05; 14M15; 14N35 | |
| dc.title | Affine approach to quantum Schubert calculus | |
| dc.type | text |