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Discrete Mathematics & Theoretical Computer Science |
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 : ScholeXplorer
IsRelatedTo ARXIV 1004.4886 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jcta.2011.01.009 Source : ScholeXplorer IsRelatedTo DOI 10.46298/dmtcs.2894 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1004.4886
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