Algebraic Combinatorics Seminar - Florian Aigner

Title: qRSt: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials

Abstract:

The Robinson--Schensted (RS) correspondence is a bijection between permutations and pairs of standard Young tableaux which plays a central role in the theory of Schur polynomials. In this talk, I will present a (q,t)-dependent probabilistic deformation of Robinson--Schensted which is related to the Cauchy identity for Macdonald polynomials. By specialising q and t, one recovers the row and column insertion algorithm as well as q- and t-deformations of RS; these have been introduced in recent years and are related to q-Whittaker and Hall-Littwood polynomials respectively. I will also explain connections to a (q,t)-generalization of the Greene--Nijenhuis--Wilf random hook walk and the q-Plancherel measure.
This is joint work with Gabriel Frieden.