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

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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
Divisions:	Faculty of Science > Mathematics Faculty of Science > Statistics
Journal or Publication Title:	Duke Mathematical Journal
Publisher:	Duke University Press
ISSN:	0012-7094
Official Date:	11 February 2014
Dates:	Date Event 11 February 2014 Available
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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