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arXiv · 2104.13846

$q{\rm RS}t$: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials (extended abstract)

Florian Aigner·Gabriel Frieden
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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.

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Florian Aigner, Gabriel Frieden. 2021-04-28. $q{\rm RS}t$: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials (extended abstract). https://arxiv.org/abs/2104.13846

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