The down operator and expansions of near rectangular k-Schur functions

Luis Serrano

Department of Mathematics, Université du Québec à Montréal, Montreal, Quebec, Canada

Department of Mathematics, Université du Québec à Montréal, Montreal, Quebec, Canada

2012/8/7 Tue 4PM-5PM

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. This can be found in arxiv:1112.4460 and arxiv:1112.4460.

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