The Annals of Probability
- Ann. Probab.
- Volume 47, Number 2 (2019), 1036-1055.
Kirillov–Frenkel character formula for loop groups, radial part and Brownian sheet
We consider the coadjoint action of a Loop group of a compact group on the dual of the corresponding centrally extended Loop algebra and prove that a Brownian motion in a Cartan subalgebra conditioned to remain in an affine Weyl chamber—which can be seen as a space time conditioned Brownian motion—is distributed as the radial part process of a Brownian sheet on the underlying Lie algebra.
Ann. Probab., Volume 47, Number 2 (2019), 1036-1055.
Received: March 2017
Revised: April 2018
First available in Project Euclid: 26 February 2019
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Defosseux, Manon. Kirillov–Frenkel character formula for loop groups, radial part and Brownian sheet. Ann. Probab. 47 (2019), no. 2, 1036--1055. doi:10.1214/18-AOP1278. https://projecteuclid.org/euclid.aop/1551171644