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arXiv · 1603.02316

Kirillov-Frenkel character formula for Loop groups, radial part and Brownian sheet

Manon Defosseux
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Abstract

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.

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BibTeXRIS

Manon Defosseux. 2016-03-07. Kirillov-Frenkel character formula for Loop groups, radial part and Brownian sheet. https://arxiv.org/abs/1603.02316

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