$qt$RSK${}^*$: A probabilistic dual RSK correspondence for Macdonald polynomials
| Autor: | Frieden, Gabriel, Schreier-Aigner, Florian |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce a probabilistic generalization of the dual Robinson--Schensted--Knuth correspondence, called $qt$RSK${}^*$, depending on two parameters $q$ and $t$. This correspondence extends the $q$RS$t$ 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. When restricting to Jack polynomials and $\{0,1\}$-matrices corresponding to words, we prove that the insertion tableaux obtained by $qt$RSK${}^*$ are invariant under swapping letters in the input word. Our approach is based on Fomin's growth diagrams and the notion of probabilistic bijections. Comment: 65 pages |
| Databáze: | arXiv |
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