Multi-state asymmetric simple exclusion processes

Understand

It is known that the Markov matrix of the asymmetric simple exclusion process (ASEP) is invariant under the Uq(sl2) 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) 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 box.