Tropical Combinatorics and Whittaker functions
By Ivan Corwin, Neil O'Connell, T. Seppalainen, Nikos Zygouras. 2011
157 citations recorded by the source corpus.
We establish a fundamental connection between the geometric 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 generalisation 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 one-dimensional directed polymer model with log-gamma weights recently introduced by one of the authors (TS).
Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/d44fa2a9c1b94787777cf5a4159db986b457f00e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Applied Mathematics
In Discrete Mathematics and Combinatorics
- Ivan Corwin
- P. Ferrari
- Alexei Borodin
- B. Vető
- L. Petrov
- Grigori Olshanski
- Jeremy Quastel
- Robert C. Dalang
Citations in the corpus
- Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, methodology): “IONS FOR DIRECTED POLYMERS 23 It follows that FN 1 (τ) = FN(τ) as defined in (1.3). The following result is shown in [51] by utilizing a continuous version of the tropical RSK correspondence (see also [24] for a discrete analog) and certain Markov kernel intertwining relations. Theorem 4.3. Fix N≥ 1,”
- Height Fluctuations for the Stationary KPZ Equation (2014, methodology): “In the spirit of the geometric lifting of the Robinson–Schensted–Knuth correspondence considered in [37, 65] (and for later use in the statement of Theorem 4.”