Hall-Littlewood RSK field

2017/05/19 by Bufetov, Alexey, Matveev, Konstantin
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.07169

Abstract

We introduce a randomized Hall-Littlewood RSK algorithm and study its combinatorial and probabilistic properties. On the probabilistic side, a new model --- the Hall-Littlewood RSK field --- is introduced. Its various degenerations contain known objects (the stochastic six vertex model, the asymmetric simple exclusion process) as well as a variety of new ones. We provide formulas for a rich class of observables of these models, extending existing results about Macdonald processes. On the combinatorial side, we establish analogs of properties of the classical RSK algorithm: invertibility, symmetry, and a "bijectivization" of the skew-Cauchy identity.

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