Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_q(D^{(2)}_{n+1}), U_q(A^{(2)}_{2n})$ and $U_q(C^{(1)}_{n})$

We introduce a homomorphism from the quantum affine algebras $U_{q} (D_{n + 1}^{(2)}), U_{q} (A_{2 n}^{(2)}), U_{q} (C_{n}^{(1)})$ to the $n$ -fold tensor product of the $q$ -oscillator algebra $A_{q}$ . Their action commute 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 $A_{q}$ . In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_{q} (D_{n + 1}^{(2)}), U_{q} (A_{2 n}^{(2)})$ and $U_{q} (C_{n}^{(1)})$

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Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_{q} (D_{n + 1}^{(2)}), U_{q} (A_{2 n}^{(2)})$ and $U_{q} (C_{n}^{(1)})$

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Tetrahedron Equation and Quantum RR Matrices for modular double of Uq(Dn+1(2)),Uq(A2n(2))Uq​(Dn+1(2)​),Uq​(A2n(2)​) and Uq(Cn(1))Uq​(Cn(1)​)

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Tetrahedron Equation and Quantum RR Matrices for modular double of Uq(Dn+1(2)),Uq(A2n(2))Uq​(Dn+1(2)​),Uq​(A2n(2)​) and Uq(Cn(1))Uq​(Cn(1)​)

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Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_{q} (D_{n + 1}^{(2)}), U_{q} (A_{2 n}^{(2)})$ and $U_{q} (C_{n}^{(1)})$

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Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_{q} (D_{n + 1}^{(2)}), U_{q} (A_{2 n}^{(2)})$ and $U_{q} (C_{n}^{(1)})$

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