Affine Lie algebras and conditioned space-time Brownian motions in affine Weyl chambers

Manon Defosseux (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We construct a sequence of Markov processes on the set of dominant weights of an affine Lie algebra g considering tensor product of irreducible highest weight modules of g and specializations of the characters involving the Weyl vector ρ. We show that it converges towards a space-time Brownian motion with a drift, conditioned to remain in a Weyl chamber associated to the root system of g. This extends in particular the results of [2] to any affine Lie algebras, in the case with a drift.

Domaines: Probabilités [math.PR]

Manon Defosseux. Affine Lie algebras and conditioned space-time Brownian motions in affine Weyl chambers. Probability Theory and Related Fields, 2016, 165, pp.649 - 665. ⟨10.1007/s00440-015-0642-8⟩. ⟨hal-01393762⟩