Combinatorial expansions for families of non-commutative k-Schur functions

TL;DR

This paper develops combinatorial expansions for non-commutative k-Schur functions using affine nilCoxeter algebra, providing new interpretations for k-Littlewood-Richardson coefficients and advancing understanding in algebraic combinatorics.

Contribution

It introduces explicit combinatorial expansions for non-commutative k-Schur functions and offers a new combinatorial interpretation for k-Littlewood-Richardson coefficients.

Findings

Explicit combinatorial expansions derived for certain non-commutative k-Schur functions.

New combinatorial interpretation for a family of k-Littlewood-Richardson coefficients.

Application of affine nilCoxeter algebra to combinatorial problems.

Abstract

We apply down operators in the affine nilCoxeter algebra to yield explicit combinatorial expansions for certain families of non-commutative k-Schur functions. This yields a combinatorial interpretation for a new family of k-Littlewood-Richardson coefficients.