TROPICAL COMBINATORICS AND WHITTAKER FUNCTIONS
TROPICAL COMBINATORICS AND WHITTAKER FUNCTIONS
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DOI：
10.1215/00127094-2410289
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发表时间：
2014-02-15
影响因子：
2.5
通讯作者：
Zygouras, Nikolaos
中科院分区：
文献类型：
--
作者：
Corwin, Ivan;O'Connell, Neil;Zygouras, Nikolaos
我们建立了几何Robinson-Schensted-Knuth（RSK）对应和GL（N，R）-Whittaker函数之间的基本联系，类似于著名的RSK对应和Schur函数之间的关系.这就产生了一个自然的家庭措施与GL（N，R）-惠特克功能，这是类似物在这种设置的舒尔措施的整数分区。柯西-利特尔伍德恒等式的相应类似物可以看作是由于Bump和Stade而得到的GL（N，R）-Whittaker函数的积分恒等式的推广。作为应用，我们得到了一个明确的积分公式的拉普拉斯变换的法律的配分函数与1维定向聚合物模型与对数伽玛权重最近推出的作者之一。
We establish a fundamental connection between the geometric Robinson-Schensted-Knuth (RSK) correspondence and GL(N,R)-Whittaker functions, analogous to the well-known relationship between the RSK correspondence and Schur functions. This gives rise to a natural family of measures associated with GL(N, R)-Whittaker functions which are the analogues in this setting of the Schur measures on integer partitions. The corresponding analogue of the Cauchy Littlewood identity can be seen as a generalization of an integral identity for GL(N, R)-Whittaker functions due to Bump and Stade. As an application, we obtain an explicit integral formula for the Laplace transform of the law of the partition function associated with a 1-dimensional directed polymer model with log-gamma weights recently introduced by one of the authors.