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

Abstract

We introduce a homomorphism from the quantum affine algebras $U_q(D_{n+1}^{(2)}),U_q(A_{2n}^{(2)}),U_q(C_n^{(1)})$ to the $n$-fold tensor product of the $q$-oscillator algebra ${\mathcal{A}}_q$. 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 ${\mathcal{A}}_q$. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

arXiv comment11 pages, minor corrections

References in corpus (7)

• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
• The vertex formulation of the Bazhanov-Baxter Model
• Cyclic monodromy matrices for sl(n) trigonometric R-matrices
• Quantum geometry of 3-dimensional lattices
• Tetrahedron and 3D reflection equations from quantized algebra of functions
• Tetrahedron Equation and Quantum R Matrices for Spin Representations of B^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}
• Tetrahedron equations and nilpotent subalgebras of U_q(sl_n)

Cited by in corpus (3)

• Matrix product formula for Macdonald polynomials
• An Ising-type formulation of the six-vertex model
• A polynomial formula for the solution of 3D reflection equation