Degrees of the stretched Kostka quasi-polynomials

TL;DR

This paper derives a uniform formula for the degree of stretched Kostka quasi-polynomials across all classical types, enhancing previous results specifically for type A.

Contribution

It introduces a type-uniform formula for the degree of stretched Kostka quasi-polynomials, extending prior work beyond type A using combinatorial models.

Findings

Provides a unified degree formula for all classical types

Improves upon previous results by McAllister for type A

Utilizes Berenstein-Zelevinsky combinatorial models

Abstract

We provide a type-uniform formula for the degree of the stretched Kostka quasi-polynomial $K_{\lambda,\mu}(N)$ in all classical types, improving a previous result by McAllister in $\mathfrak{sl}_r(\mathbb{C})$. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky.