Stochastic $R$ matrix for $U_q(A^{(1)}_n)$
Quantum Algebra
2016-11-23 v4 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We show that the quantum matrix for symmetric tensor representations of 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 -Hahn process for . Based on these results we formulate new discrete and continuous time integrable Markov processes on a one-dimensional chain in terms of species of particles obeying asymmetric stochastic dynamics. Bethe ansatz eigenvalues of the Markov matrices are also given.
Cite
@article{arxiv.1604.08304,
title = {Stochastic $R$ matrix for $U_q(A^{(1)}_n)$},
author = {Atsuo Kuniba and Vladimir V. Mangazeev and Shouya Maruyama and Masato Okado},
journal= {arXiv preprint arXiv:1604.08304},
year = {2016}
}
Comments
21 pages. Remark 9 added, Typos in Appendix A fixed