An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations

Understand

A recent paper \cite{KMMO} introduced the stochastic U_q(A_n^{(1)}) vertex model.

• The stochastic S-matrix is related to the R-matrix of the quantum group U_q(A_n^{(1)}) by a gauge transformation.
• We will show that a certain function D^+_{\mu} intertwines with the transfer matrix and its space reversal.
• When interpreting the transfer matrix as the transition matrix of a discrete-time totally asymmetric particle system on the one-dimensional lattice Z, the function D^+_{\mu} becomes a Markov duality function D_{\mu} which only depends on q and the vertical spin parameters \mu_x.