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Please use this identifier to cite or link to this item: http://hdl.handle.net/1860/1940

Title: Quantum cohomology and the k-Schur basis
Authors: Morse, Jennifer
Lapointe, Luc
Issue Date: 27-May-2005
Citation: Retrieved October 30, 2007 from http://xxx.lanl.gov/find/grp_math/1/au:+Morse_J/0/1/0/all/0/1
Abstract: 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 csu(ℓ) 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.
URI: http://lanl.arxiv.org/abs/math/0501529v2
Appears in Collections:Faculty Research and Publications (Mathematics)

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