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

TL;DR

This paper provides explicit combinatorial formulas for expanding k-Schur functions associated with maximal rectangles within the affine nilCoxeter algebra, and establishes their commutation relations with algebra generators.

Contribution

It introduces new combinatorial formulas for k-Schur functions indexed by maximal rectangles and proves their commutation relations within the affine nilCoxeter algebra.

Findings

Explicit formulas for k-Schur functions indexed by maximal rectangles

Commutation relations between k-Schur functions and affine nilCoxeter algebra generators

Enhanced understanding of the algebraic structure of k-Schur functions

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.