Littelmann paths and brownian paths

Abstract

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.

30 pages, 1 figure

Cited by in corpus (40)

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• Random walks in Weyl chambers and crystals
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• Whittaker functions and related stochastic processes
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• Skew-product representations of multidimensional Dunkl Markov processes
• RSK in last passage percolation: a unified approach
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• Constructing discrete harmonic functions in wedges
• Whittaker processes and Landau-Ginzburg potentials for flag manifolds
• Positive temperature dynamics on Gelfand-Tsetlin patterns restricted by wall
• Littelmann path model for geometric crystals
• Growth estimates for discrete quantum groups
• Edge Universality for Nonintersecting Brownian Bridges
• Central measures on multiplicative graphs, representations of Lie algebras and weight polytopes
• Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion
• Beta-gamma algebra identities and Lie-theoretic exponential functionals of Brownian motion
• The affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ and a conditioned space-time Brownian motion
• Boundary behavior for random walks in cones
• Maximum of Dyson Brownian motion and non-colliding systems with a boundary
• Kirillov-Frenkel character formula for Loop groups, radial part and Brownian sheet
• Conditioned one-way simple random walk and representation theory
• Separation cutoffs for random walk on irreducible representations
• Reciprocal of the First hitting time of the boundary of dihedral wedges by a radial Dunkl process
• A family of centered random walks on weight lattices conditioned to stay in Weyl chambers
• Tensor Product Markov Chains
• Convergence rates of random walk on irreducible representations of finite groups
• Determinantal Martingales and Interacting Particle Systems
• Brownian paths in an alcove and the Littelmann path model
• Affine Dunkl processes
• A common limit in large rank for Markov chains defined from representations of classical Lie algebras