|Date: Friday, October 07, 2011
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: sl(2) operators and Markov dynamics on branching graphs
Abstract: Back in the 1980s, S.Fomin and R.Stanley observed that certain commutation relations between linear operators associated with a graded poset (or a graded graph) lead to enumerative results and combinatorial correspondences. In the last decade, A. Borodin, J.Fulman, A.Okounkov, G.Olshanski, and myself used more general commutation relations to study probability measures and Markov processes on partitions.
I will start with operators satisfying sl(2) commutation relations as in Okounkov's paper, and use them to give a new characterization of important measures on partitions. Examples include the two-parameter Poisson-Dirichlet distributions as well as measures coming from representation theory of the infinite symmetric group. I will then explain how these sl(2) operators can be used to describe and study Markov dynamics on partitions in these examples in a unified manner.
Speaker: Leonid Petrov
Institution: Northeastern U.