A $q$-boson representation of Zamolodchikov-Faddeev algebra for stochastic $R$ matrix of $U_q(A_n^{(1)})$

Abstract

We construct a $q$-boson representation of the Zamolodchikov-Faddeev algebra whose structure function is given by the stochastic $R$ matrix of $U_q(A_n^{(1)})$ introduced recently. The representation involves quantum dilogarithm type infinite products in the $n(n-1)/2$-fold tensor product of $q$-bosons. It leads to a matrix product formula of the stationary probabilities in the $U_q(A_n^{(1)})$-zero range process on a one-dimensional periodic lattice.

13 pages. Minor changes

References in corpus (5)

• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Matrix product formula for Macdonald polynomials
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Cited by in corpus (4)

• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• The non-compact XXZ spin chain as stochastic particle process
• Integrable Structure of Multispecies Zero Range Process
• Density and current profiles in $U_q(A_2^{(1)})$ zero range process