Time: 9h00, Wednesday, April 5, 2017
Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Kashiwara crystal basis theory allow to associate a random walk to each minuscule irreducible representation V of a simple Lie algebra; the generalized Pitman transform for similar random walks with uniform distributions yields yet a Markov chain when the crystal attached to $V$ is endowed with a probability distribution compatible with its weight graduation.

First, I will present the notion of Pitman transform for the Brownian motion on the real line and the simple random walk on Z. 
Then, I will explain how we can generalize this transformation in higher dimension, using the irreducible representations of sl(n, C), crystals and semi-standart tableaux. I will present an explicit example on sl(2, C) which can be computed using insertion schemes on tableaux.
The main probabilistic argument in the proof is a quotient version of a renewal theorem that we obtained in the context of general random walks in a lattice.
(joint work with C. Lecouvey  and E. Lesigne)