Character formulae of sl̂n-modules and inhomogeneous paths

摘要: Abstract Let B(l) be the perfect crystal for l-symmetric tensor representation of quantum affine algebra U q ′ ( sl n ) . For a partition μ = (μ1, …, μm, elements product B(μ1) ⊗…⊗ B(μm) can regarded as inhomogeneous paths. We establish bijection between certain large limit this and an (generally reducible) integrable )- module , which forms family depending on inhomogeneity kept in limit. associated one-dimensional sums, relations with Kostka-Foulkes polynomials are clarified, new fermionic formulae presented. By combining their limits bijection, we prove or conjecture several string functions, branching coset functions spinon character formula both vertex RSOS types.