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arXiv · 1604.08304

Stochastic $R$ matrix for $U_q(A^{(1)}_n)$

Atsuo Kuniba·Vladimir V. Mangazeev·Shouya Maruyama·Masato Okado
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Abstract

We show that the quantum $R$ matrix for symmetric tensor representations of $U_q(A^{(1)}_n)$ 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.

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Atsuo Kuniba, Vladimir V. Mangazeev, Shouya Maruyama, Masato Okado. 2016-06-21. Stochastic $R$ matrix for $U_q(A^{(1)}_n)$. https://doi.org/10.1016/j.nuclphysb.2016.09.016

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