Seminar on Combinatorics, Lie Theory, and Topology
# qtRSK*: A probabilistic dual RSK correspondence for Macdonald polynomials

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Europe/Rome

Aula G (Department of Mathematics)
### Aula G

#### Department of Mathematics

Description

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.