QUANTUM COHOMOLOGY AND THE k-SCHUR BASIS
In: Transactions of the American Mathematical Society, Jg. 360 (2008), Heft 4, S. 2021-2040
Online
academicJournal
- print, 33 ref
Zugriff:
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 su(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.
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QUANTUM COHOMOLOGY AND THE k-SCHUR BASIS
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Autor/in / Beteiligte Person: | LAPOINTE, Luc ; MORSE, Jennifer |
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Zeitschrift: | Transactions of the American Mathematical Society, Jg. 360 (2008), Heft 4, S. 2021-2040 |
Veröffentlichung: | Providence, RI: American Mathematical Society, 2008 |
Medientyp: | academicJournal |
Umfang: | print, 33 ref |
ISSN: | 0002-9947 (print) |
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