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

2011/12/19 by Chris Berg, Berg, Chris, Franco Saliola +3
Mathematics · #05E05 #14N15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E05 #msc:14N15

paper · pdf · doi:10.48550/arxiv.1112.4460

arxiv created 2012/02/17 · arxiv updated 2012/02/20

Abstract

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.

Related

• Combinatorial expansions for families of non-commutative k-Schur functions
• Pieri operators on the affine nilCoxeter algebra
• Skew Littlewood-Richardson rules from Hopf algebras
• Reduced Schur Functions and the Littlewood-Richardson Coefficients
• A Littlewood-Richardson Rule for factorial Schur functions