Seminar on Combinatorics, Lie Theory, ​and Topology

qtRSK*: A probabilistic dual RSK correspondence for Macdonald polynomials

by Florian Schreier-Aigner (Universität Wien)

Aula G (Department of Mathematics)

Aula G

Department of Mathematics


We introduce a probabilistic generalization of the dual Robinson--Schensted--Knuth correspondence, called qtRSK∗, depending on two parameters $q$ and $t$. This correspondence extends our recently introduced qRSt correspondence and allows the first tableaux-theoretic proof of the dual Cauchy identity for Macdonald polynomials. By specializing $q$ and $t$, one recovers the row and column insertion version of the classical dual RSK correspondence as well as of $q$- and $t$-deformations thereof which are connected to q-Whittaker and Hall--Littlewood polynomials, but also a novel correspondence for Jack polynomials.

The talk is based on joint work with Gabriel Frieden.