The Kostka coefficient K_{λ,μ} is the dimension of the weight space V^λ(μ) in the irreducible representation V^λ of a complex semisimple Lie algebra. We provide a type-uniform formula for the degrees of the stretched Kostka quasi-polynomials K_{λ,μ}(N):= K_{Nλ,Nμ} in all classical types, improving and extending a previous result by McAllister in type A. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky. This is based on joint work with Yibo Gao.
