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Kirillov-Frenkel character formula for loop groups, radial part and Brownian sheet. (English) Zbl 07053563
Summary: 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.
MSC:
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
60J65 Brownian motion
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