2011/10/31 by Ivan Corwin, Neil O'Connell, Neil O’Connell +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Connection (principal bundle) #Generalization #Identity (music) #Integer (computer science) #Laplace transform #Mathematical functions and polynomials #Partition (number theory) #Partition function (quantum field theory) #Symmetric function #cond-mat.stat-mech #math-ph #math.CO #math.MP #math.PR #math.RT
paper · pdf · doi:10.1215/00127094-2410289
published as Duke Math. J. 163, no. 3 (2014), 513-563 · 31 pages,6 figures, updated introduction
arxiv created 2013/05/13 · openalex publication_date 2014/02/11 · arxiv updated 2015/01/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.