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Littelmann paths and Brownian paths. (English) Zbl 1161.60330
Summary: We study some path transformations related to Pitman’s theorem [J. W. Pitman, Adv. Appl. Probab. 7, 511–526 (1975; Zbl 0332.60055), Theorem 1.3] on Brownian motion and the three-dimensional Bessel process. We relate these to the Littelmann path model [see P. Littelmann, Ann. Math. (2) 142, No. 3, 499–525 (1995; Zbl 0858.17023)] and give applications to representation theory and to Brownian motion in a Weyl chamber

MSC:
60J65 Brownian motion
05E10 Combinatorial aspects of representation theory
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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