An algebraic construction of duality functions for the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model and its degenerations
In [\textit{A. Kuniba} et al., Nucl. Phys., B 913, 248--277 (2016; Zbl 1349.81115)], the authors introduced the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model. In the paper under review, the author shows that the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model is dual to its space reversal with respect to a certain explicit duality function \(D_{\vec{m}}\). It is shown that the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model is an \(n\)-species generalization of the models of \textit{I. Corwin} and \textit{L. Petrov} [Commun. Math. Phys. 343, No. 2, 651--700 (2016; Zbl 1348.82055)] and \textit{A. Borodin} and \textit{L. Petrov} [Sel. Math., New Ser. 24, No. 2, 751--874 (2018; Zbl 1405.60141)]. It is also shown that the multi-species \(q\)-Hahn Boson process, which arises at a special value of the spectral parameter, also satisfies duality with respect to \(D_{\infty},\) generalizing the single-species result of \textit{I. Corwin} [Int. Math. Res. Not. 2015, No. 14, 5577--5603 (2015; Zbl 1335.82018)].
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