Duke Mathematical Journal· 2014Q1
Tropical combinatorics and Whittaker functions
- 91citations
- Q1SCImago
- 2014year
Short summary
A new connection is established between the Robinson-Schensted-Knuth (RSK) correspondence and GL(N,R)-Whittaker functions, analogous to the known link with Schur functions.
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Key points
- Establishes a connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions.
- Introduces new measures associated with GL(N,R)-Whittaker functions, analogous to Schur measures.
- Generalizes the Cauchy-Littlewood identity for GL(N,R)-Whittaker functions.
- Provides an explicit integral formula for the Laplace transform of a partition function in a log-gamma weighted directed polymer model.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Duke Mathematical Journal, 2014 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics