Quantum cohomology and the k-Schur basis
| dc.creator | Lapointe, L. | |
| dc.creator | Morse, J. | |
| dc.date | 2005-01-28 | |
| dc.date | 2005-05-27 | |
| dc.date.accessioned | 2026-07-07T05:16:31Z | |
| dc.date.available | 2026-07-07T05:16:31Z | |
| dc.description | We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions. As a consequence, both the 3-point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to \hat{su}(\ell) are shown to be k-Littlewood Richardson coefficients. From this, Mark Shimozono conjectured that the k-Schur functions form the Schubert basis for the homology of the loop Grassmannian, whereas k-Schur coproducts correspond to the integral cohomology of the loop Grassmannian. We introduce dual k-Schur functions defined on weights of k-tableaux that, given Shimozono's conjecture, form the Schubert basis for the cohomology of the loop Grassmannian. We derive several properties of these functions that extend those of skew Schur functions. | |
| dc.description | 20 pages, revised version with minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0501529 | |
| dc.identifier | http://arxiv.org/abs/math/0501529 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74014 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 05EXX, 14N35,17B37 | |
| dc.title | Quantum cohomology and the k-Schur basis | |
| dc.type | text |