Séminaire Lotharingien de Combinatoire, 91B.75 (2024), 12 pp.
Gabriel Frieden and Florian Schreier-Aigner
qtRSK*: A Probabilistic Dual RSK Correspondence for Macdonald Polynomials
Abstract.
We introduce a probabilistic generalization of the dual
Robinson-Schensted-Knuth correspondence, called qtRSK*,
depending on two parameters q and t. This correspondence extends
the qRSt correspondence, recently introduced by the authors,
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.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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