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Probability Theory and Related Fields

, Volume 165, Issue 3–4, pp 649–665 | Cite as

Affine Lie algebras and conditioned space-time Brownian motions in affine Weyl chambers

  • Manon Defosseux
Article
  • 106 Downloads

Abstract

We construct a sequence of Markov processes on the set of dominant weights of an affine Lie algebra \(\mathfrak {g}\) considering tensor product of irreducible highest weight modules of \(\mathfrak {g}\) and specializations of the characters involving the Weyl vector \(\rho \). We show that it converges towards a space-time Brownian motion with a drift, conditioned to remain in a Weyl chamber associated to the root system of \(\mathfrak {g}\). This extends in particular the results of Defosseux (arXiv:1401.3115, 2014) to any affine Lie algebras, in the case with a drift.

Mathematics Subject Classification

17B67 35R37 60J65 

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Appliquées à Paris 5, Université Paris 5ParisFrance

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