KOSTKA-FOULKES POLYNOMIALS AND CRYSTAL GRAPHS OF QUANTUM GROUPS OF TYPE A(N)

Alain Lascoux (1) , B Leclerc , Jean-Yves Thibon

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

We describe the Kostka-Foulkes polynomials K-lambda mu, (q), i.e. the q-analogues of weight multiplicities in the irreducible sl(n, C)-modules V-lambda, by means of the geometry of the crystal graph associated to V-lambda. We obtain in this way a refinement of the generalized exponents of sl(n, C).

Domaines: Physique mathématique [math-ph]

Alain Lascoux, B Leclerc, Jean-Yves Thibon. KOSTKA-FOULKES POLYNOMIALS AND CRYSTAL GRAPHS OF QUANTUM GROUPS OF TYPE A(N). Comptes rendus de l'Académie des sciences. Série I, Mathématique, 1995, 320 (2), pp.131--134. ⟨hal-00693529⟩