Multi-state Asymmetric Simple Exclusion Processes

It is known that the Markov matrix of the asymmetric simple exclusion process (ASEP) is invariant under the Uq(sl2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_q(sl_2)$$\end{document} algebra. This is the result of the fact that the Markov matrix of the ASEP coincides with the generator of the Temperley–Lieb (TL) algebra, the dual algebra of the Uq(sl2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_q(sl_2)$$\end{document} algebra. Various types of algebraic extensions have been considered for the ASEP. In this paper, we considered the multi-state extension of the ASEP, by allowing more than two particles to occupy the same site. We constructed the Markov matrix by dimensionally extending the TL generators and derived explicit forms of particle densities and currents on steady states. Then we showed how decay lengths differ from the original two-state ASEP under closed boundary conditions.