The Annals of Probability

Kirillov–Frenkel character formula for loop groups, radial part and Brownian sheet

Manon Defosseux

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 60J65: Brownian motion [See also 58J65]

Kirillov character formula loop group Brownian sheet radial part Doob transform Brownian motion in affine Weyl chamber


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.

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