Abstract
We introduce a homomorphism from the quantum affine algebras \({U_q(D^{(2)}_{n+1}), U_q (A^{(2)}_{2n})}\), \({U_q(C^{(1)}_{n})}\) to the n-fold tensor product of the q-oscillator algebra \({\mathcal{A}_q}\). Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of \({\mathcal{A}_q}\). In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.
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Kuniba, A., Okado, M. & Sergeev, S. Tetrahedron Equation and Quantum R Matrices for Modular Double of \({{\varvec{{U_q(D^{(2)}_{n+1})}}, \varvec{{U_q (A ^{(2)}_{2n})}}}}\) and \(\varvec{{U_q(C^{(1)}_{n})}}\) . Lett Math Phys 105, 447–461 (2015). https://doi.org/10.1007/s11005-015-0747-0
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DOI: https://doi.org/10.1007/s11005-015-0747-0