Hall–Littlewood RSK field

TY - JOUR

T1 - Hall–Littlewood RSK field

AU - Bufetov, Alexey

AU - Matveev, Konstantin

N1 - Publisher Copyright: © 2018, Springer Nature Switzerland AG.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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.

KW - Hall–Littlewood polynomials

KW - Macdonald processes

KW - RSK algorithm

KW - Six vertex model

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U2 - 10.1007/s00029-018-0442-y

DO - 10.1007/s00029-018-0442-y

M3 - Article

SN - 1022-1824

VL - 24

SP - 4839

EP - 4884

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 5

ER -