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

2016/03/07 by Manon Defosseux, Defosseux, Manon
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1603.02316

18 pages, 1 figure

arxiv created 2016/03/07 · openalex publication_date 2016/03/07 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The affine Lie algebra \mathfraksl₂(\C) and a conditioned space-time Brownian motion

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