## Berg, Chris and Saliola, Franco and Serrano, Luis - 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)
The down operator and expansions of near rectangular k-Schur functions

Authors: Berg, Chris and Saliola, Franco and Serrano, Luis

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.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: affine Schubert calculus, dual graded graphs,symmetric functions, k-Schur functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]