论文标题
美元
$q{\rm RS}t$: A probabilistic Robinson--Schensted correspondence for Macdonald polynomials
论文作者
论文摘要
我们提出了罗宾逊 - 链式对应关系的概率概括，其中置换映射到具有非零概率的几对不同的标准年轻tableaux。概率取决于两个参数$ q $和$ t $，该通信为MacDonald多项式的Cauchy身份的无平方部分提供了新的证明（即，$ x_1 \ cdots x_n y_1 y_1 \ cdots y__n $的系数的平等，与persiantations和标准的年轻人相关。通过以各种方式专门使用$ q $和$ t $，可以恢复罗宾逊 - 插入通讯的行和列插入版，几个$ q $ - 和$ t $ to-t $ - 插入的$ q $ - 插入，这些版本与$ q $ $ q $ - 惠特克和霍尔 - 洛尔特伍德流程以及Plancherel On Carteritials On Carteritionals torteritions一起引入了近年来。我们的构建基于Fomin的生长图，以及最近引入的加权集之间的概率生命的概念。
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.
