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Quantum cohomology and the k-Schur basis
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http://hdl.handle.net/1860/1940
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| 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
http://hdl.handle.net/1860/1940 |
| Appears in Collections: | Faculty Research and Publications (Mathematics)
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