Positive combinatorial formulas for Kostka–Foulkes polynomials beyond type A

Derive positive combinatorial formulas for Kostka–Foulkes polynomials, or q-analogues of weight multiplicities, for Lie types beyond type A_{n-1}.

Background

The paper explains that atomic decompositions of crystals are relevant to computing positive combinatorial formulas for Kostka–Foulkes polynomials. While such formulas are discussed in the context of type A_{n-1}, the corresponding problem beyond type A_{n-1} is identified as unresolved. This provides motivation for studying atomic decompositions and crystal embeddings as tools that may eventually extend positive formulas to other Lie types.