Selecta Mathematica

, Volume 24, Issue 5, pp 4839–4884 | Cite as

Hall–Littlewood RSK field

  • Alexey Bufetov
  • Konstantin Matveev


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.


Hall–Littlewood polynomials RSK algorithm Macdonald processes Six vertex model 

Mathematics Subject Classification

Primary 05E05 Secondary 60K35 


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We are grateful to A. Borodin for useful discussions. We are grateful to I. Corwin for useful comments. We are grateful to referees for their useful remarks. A. Bufetov was partially supported by The Foundation Sciences Mathematiques de Paris.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA

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