CRYSTAL GRAPHS AND Q-ANALOGS OF WEIGHT MULTIPLICITIES FOR THE ROOT-SYSTEM A(N)

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

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

We give an expression of the q-analogues of the multiplicities of weights in irreducible sl(n+1)-modules in terms of the geometry of the crystal graph attached to corresponding U-q(sl(n+1))-modules. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight refining Kostant's generalized exponents.

Domaines: Physique Classique [physics.class-ph]

Alain Lascoux, B Leclerq, Jean-Yves Thibon. CRYSTAL GRAPHS AND Q-ANALOGS OF WEIGHT MULTIPLICITIES FOR THE ROOT-SYSTEM A(N). Letters in Mathematical Physics, 1995, 35 (4), pp.359--374. ⟨10.1007/BF00750843⟩. ⟨hal-00693520⟩