Affine Lie algebras and a conditioned space-time Brownian motion in an affine Weyl chamber

Abstract

We construct a sequence of Markov processes on the set of dominant weights of an affine Lie algebra $\mathfrak{g}$ considering tensor product of irreducible highest weight modules of $\mathfrak{g}$ and specializations of the characters involving the Weyl vector $\rho$. 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 $\mathfrak{g}$.

Probab. Theory Relat. Fields, 2015

Cited by in corpus (2)

• Martin boundary of a space-time Brownian motion with drift killed at the boundary of a moving cone
• Reflected Brownian Motion in a wedge: sum-of-exponential absorption probability at the vertex and differential properties