## Abstract

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.

Original language | English |
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Pages (from-to) | 513-563 |

Number of pages | 51 |

Journal | Duke Mathematical Journal |

Volume | 163 |

Issue number | 3 |

DOIs | |

Publication status | Published - 15 Feb 2014 |