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15 January Friday

Gabriel Frieden (UQAM): qRSt: A probabilistic Robinson–Schensted correspondence for Macdonald polynomials

15 January 2021, 11:00 - 15 January 2021, 12:00
En ligne/online, Canada

Résumé: 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 recent years, several probabilistic q-RS and t-RS algorithms have been introduced; these are probabilistic deformations of Robinson–Schensted in which a permutation maps to several different pairs of tableaux, with probabilities depending on the parameter q or t. These algorithms are related to q-Whittaker and Hall–Littlewood polynomials, and they have applications to probabilistic models such as the TASEP and stochastic six-vertex model.

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 specializing q and t in various ways, one recovers the above-mentioned q-RS and t-RS maps, as well as both the row and column insertion versions of RS itself. I will also explain how part of the construction can be understood in terms of a (q,t)-generalization of the Greene–Nijenhuis–Wilf random hook walk.

This is joint work with Florian Aigner.

Details
Date: 15 January 2021
Time: 11 h 00 min - 12 h 00 min
Venue
Venue Name: En ligne/online
Address: Canada