coefficients, see [@lidskii82; @knutson00; @christandl08].

Our main results in this context are quantized versions of our earlier theorems: Kronecker coefficients can be computed by applying finite difference operators to weight multiplicities which are related to the classical marginal problem: Instead of measuring the volume of a polytope, one has to count the number of lattice points in the polytope. This can be computed efficiently using Barvinok’s algorithm [@barvinok94], and so leads to an efficient algorithm for computing Kronecker coefficients for Young diagrams with bounded height. Again, we shall establish the results in greater generality and recover the version for Kronecker coefficients as a special case.

Notation and Conventions {#notation}
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Throughout this article, $K$ will denote a compact, connected Lie group with maximal torus $T \subseteq K$, rank $r = \dim T$, Weyl group $W$, respective Lie algebras $\mathfrak k$ and $\mathfrak t$, and integral lattice $\Lambda = \ker {\left.\exp\vphantom{\big|}\right|_{\mathfrak t}}$ [@cartersegalmacdonald95; @kirillov08]. We write $\pi_{K,T} \colon \mathfrak k^* \rightarrow \mathfrak t^*$ for the projection dual to the inclusion $\mathfrak t \subseteq \mathfrak k$. We will think of weights as elements of the dual lattice, $\Lambda^* = \operatorname{Hom}_{{\mathbb Z}}(\Lambda, {\mathbb Z}) \subseteq \mathfrak t^*$, and identify a character $\chi \colon 