Stochastic R matrix for Uq(An (1))

A. Kuniba*, V. V. Mangazeev, S. Maruyama, M. Okado

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    38 Citations (Scopus)

    Abstract

    We show that the quantum R matrix for symmetric tensor representations of Uq(An (1)) satisfies the sum rule required for its stochastic interpretation under a suitable gauge. Its matrix elements at a special point of the spectral parameter are found to factorize into the form that naturally extends Povolotsky's local transition rate in the q-Hahn process for n=1. Based on these results we formulate new discrete and continuous time integrable Markov processes on a one-dimensional chain in terms of n species of particles obeying asymmetric stochastic dynamics. Bethe ansatz eigenvalues of the Markov matrices are also given.

    Original languageEnglish
    Pages (from-to)248-277
    Number of pages30
    JournalNuclear Physics B
    Volume913
    DOIs
    Publication statusPublished - 1 Dec 2016

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