On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers (Q909808)

The decomposition into irreducible components of the tensor product of the representations of gl(n) by making use of the combinatorics of Young diagrams (tableaux, bitableaux, supertableaux) is considered. The formulas for the multiplicity of weights for irreducible tensor representations of the Lie supergroup GL(M/N) as well as for explicitly calculating the Kostka-Green-Foulkes polynomials corresponding to the Young supertableaux are given. As a consequence a new rule for finding the Clebsch-Gordan numbers is deduced.