A concise proof of cylindric Schur positivity

TL;DR

This paper provides a concise proof demonstrating that cylindric Schur functions expand positively into non-skew cylindric Schur functions, with coefficients identified as fusion coefficients.

Contribution

It introduces a short proof of cylindric Schur positivity and clarifies the nature of the expansion coefficients as fusion coefficients.

Findings

Skew cylindric Schur functions expand positively in terms of non-skew cylindric Schur functions.

Expansion coefficients are identified as fusion coefficients.

The proof is notably concise compared to previous approaches.

Abstract

Cylindric Schur functions are a family of symmetric functions that generalize skew Schur functions. We give a short proof that skew cylindric Schur functions expand positively in terms of non-skew cylindric Schur functions. In particular, we show that the expansion coefficients are fusion coefficients.