부산대학교 도서관

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 (i.e. the equality of the coefficients of |$x_1 \cdots x_n y_1 \cdots y_n$| on either side, which are related to permutations and standard Young tableaux). By specializing |$q$| and |$t$| in various ways, one recovers the row and column insertion versions of the Robinson–Schensted correspondence, several |$q$| - and |$t$| -deformations of row and column insertion which have been introduced in recent years in connection with |$q$| -Whittaker and Hall–Littlewood processes, and the Plancherel measure on partitions. Our construction is based on Fomin's growth diagrams and the recently introduced notion of a probabilistic bijection between weighted sets. [ABSTRACT FROM AUTHOR]