Séminaire Lotharingien de Combinatoire, 85B.79 (2021), 12 pp.

Florian Aigner and Gabriel Frieden

qRSt: A Probabilistic Robinson-Schensted Correspondence for Macdonald Polynomials

Abstract. We present a probabilistic generalization of the Robinson-Schensted correspondence in which a permutation maps to several different pairs of standard Young tableaux with nonzero probability. The probabilities depend on two parameters q and t, and the correspondence gives a new proof of the squarefree part of the Cauchy identity for Macdonald polynomials. By specializing q and t in various ways, one recovers both the row and column insertion versions of the Robinson-Schensted correspondence, as well as several q- and t-deformations of row and column insertion which have been introduced in recent years in connection with integrable probability.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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