Title: Tetrahedron Equation and Quantum R Matrices for Modular Double of $${{\varvec{{U_q(D^{(2)}_{n+1})}}, \varvec{{U_q (A ^{(2)}_{2n})}}}}$$ U q ( D n + 1 ( 2 ) ) , U q ( A 2 n ( 2 ) ) and $$\varvec{{U_q(C^{(1)}_{n})}}$$ U q ( C n ( 1 ) )
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.