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YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS

Part of: Equilibrium statistical mechanics Special processes Combinatorial probability Algebraic combinatorics

Published online by Cambridge University Press:  31 October 2019

ALEXEY BUFETOV  and
LEONID PETROV
ALEXEY BUFETOV
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; alexey.bufetov@gmail.com
LEONID PETROV
Affiliation:
University of Virginia, Department of Mathematics, 141 Cabell Drive, Kerchof Hall, P.O. Box 400137, Charlottesville, VA 22904, USA Institute for Information Transmission Problems, Bolshoy Karetny per. 19, Moscow 127994, Russia; lenia.petrov@gmail.com

Abstract

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Employing bijectivization of summation identities, we introduce local stochastic moves based on the Yang–Baxter equation for $U_{q}(\widehat{\mathfrak{sl}_{2}})$. Combining these moves leads to a new object which we call the spin Hall–Littlewood Yang–Baxter field—a probability distribution on two-dimensional arrays of particle configurations on the discrete line. We identify joint distributions along down-right paths in the Yang–Baxter field with spin Hall–Littlewood processes, a generalization of Schur processes. We consider various degenerations of the Yang–Baxter field leading to new dynamic versions of the stochastic six-vertex model and of the Asymmetric Simple Exclusion Process.

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60C05: Combinatorial probability 05E05: Symmetric functions and generalizations 82B23: Exactly solvable models; Bethe ansatz
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e39
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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