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Tropical combinatorics and Whittaker functions
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Corwin, Ivan, O’Connell, Neil, Seppäläinen, Timo and Zygouras, Nikolaos (2014) Tropical combinatorics and Whittaker functions. Duke Mathematical Journal, Volume 163 (Number 3). pp. 513-563. doi:10.1215/00127094-2410289 ISSN 0012-7094.
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Official URL: http://dx.doi.org/10.1215/00127094-2410289
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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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Journal or Publication Title: | Duke Mathematical Journal | ||||
Publisher: | Duke University Press | ||||
ISSN: | 0012-7094 | ||||
Official Date: | 11 February 2014 | ||||
Dates: |
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Volume: | Volume 163 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 513-563 | ||||
DOI: | 10.1215/00127094-2410289 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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