Factorization formulas of $K$-$k$-Schur functions II

TL;DR

This paper provides detailed proofs of explicit factorization formulas for $K$-$k$-Schur functions related to multiple $k$-rectangles, advancing the understanding of their algebraic structure.

Contribution

It offers complete proofs of factorization formulas for $K$-$k$-Schur functions associated with multiple $k$-rectangles, building on previous work.

Findings

Explicit factorization formulas for $K$-$k$-Schur functions are established.

The paper confirms the algebraic structure of these functions in the context of multiple $k$-rectangles.

Provides rigorous proofs supporting the formulas from prior conjectures or partial results.

Abstract

Subsequently to the author's preceding paper, we give full proofs of some explicit formulas about factorizations of $K$-$k$-Schur functions associated with any multiple $k$-rectangles.