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Discrete Mathematics & Theoretical Computer Science |
Chris Berg ; Franco Saliola ; Luis Serrano - The down operator and expansions of near rectangular k-Schur functions
dmtcs:3052 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3052The down operator and expansions of near rectangular k-Schur functionsConference paper
Authors: Chris Berg 1,2,3; Franco Saliola 
4,3; Luis Serrano 3
- 1 Fields Institute for Research In Mathematical Sciences
- 2 York University [Toronto]
- 3 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
- 4 Fields Institute for Research In Mathematical Sciences
We prove that the Lam-Shimozono ``down operator'' on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of ``near rectangles'' in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of the corresponding k-Littlewood–Richardson coefficients.
Source: HAL:hal-01283162v1
Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: symmetric functions, k-Schur functions, affine Schubert calculus, dual graded graphs,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
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