Stochastic R matrix for Uq(An(1))

2016/04/30 by Atsuo Kuniba, Vladimir V. Mangazeev, Shouya Maruyama +1 · 53 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bethe ansatz #Chemistry #Combinatorics #Eigenvalues and eigenvectors #Integrable system #Markov chain #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random matrix #Statistical physics #Statistics #Tensor (intrinsic definition) #Tensor decomposition and applications #math-ph #math.MP #math.QA #msc:60C99 #msc:81R50 #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2016.09.016

published in Nuclear Physics B 913, 248-277 (Elsevier BV) · 21 pages. Remark 9 added, Typos in Appendix A fixed

arxiv created 2016/06/21 · openalex created_date 2016/06/24 · openalex publication_date 2016/09/29 · arxiv updated 2016/11/23 · openalex updated_date 2026/08/05

Abstract

We show that the quantum R matrix for symmetric tensor representations of U q ( A n ( 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.

Citations

• Algebraic construction of multi-species q-Boson system
• A deformation of affine Hecke algebra and integrable stochastic particle system
• Zamolodchikov's tetrahedron equation and hidden structure of quantum groups
• The vertex formulation of the Bazhanov-Baxter model

Cited by

• Boundary matrices for the higher spin six vertex model
• Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model