|Date: Friday, February 17, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Tropical combinatorics and Whittaker functions
Abstract: The Robinson-Schensted-Knuth (RSK) correspondence is a combinatorial mapping which plays a fundamental role in the theory of Young tableaux, symmetric functions, ultra-discrete integrable systems and representation theory. It is also the basic structure that lies behind the `solvability' of a particular family of combinatorial models in probability and statistical physics which include longest increasing subsequence problems, directed last passage percolation in 1+1 dimensions, the totally asymmetric exclusion process, queues in series and discrete models for surface growth. There is a geometric version of the RSK correspondence introduced by A.N. Kirillov, known as the `tropical RSK correspondence'. We show that, with a particular family of product measures on its domain, the tropical RSK correspondence is closely related to GL(N,R)-Whittaker functions and yields analogues in this setting of the Schur measures and Schur processes on integer partitions.
This is based on joint work with Neil O'Connell, Timo Seppalainen and Nikos Zygouras.
Speaker: Ivan Corwin
Institution: Microsoft and MIT