Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra

Abstract

We give several explicit combinatorial formulas for the expansion of k-Schur functions indexed by maximal rectangles in terms of the standard basis of the affine nilCoxeter algebra. Using our result, we also show a commutation relation of k-Schur functions corresponding to rectangles with the generators of the affine nilCoxeter algebra.

to appear in Journal of Combinatorics, 28 pages

References in corpus (1)

• Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions

Cited by in corpus (4)

• $k$-Schur functions and affine Schubert calculus
• Fomin-Greene monoids and Pieri operations
• Expansions of $k$-Schur functions in the affine nilCoxeter algebra
• Symmetries on the lattice of $k$-bounded partitions