Tetrahedron Equation and Quantum R Matrices for Spin Representations of B^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}

Abstract

It is known that a solution of the tetrahedron equation generates infinitely many solutions of the Yang-Baxter equation via suitable reductions. In this paper this scheme is applied to an oscillator solution of the tetrahedron equation involving bosons and fermions by using special 3d boundary conditions. The resulting solutions of the Yang-Baxter equation are identified with the quantum R matrices for the spin representations of B^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}.

17 pages, 7 figures, minor misprint corrected

References in corpus (3)

• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
• Quantum geometry of 3-dimensional lattices
• Super-tetrahedra and super-algebras

Cited by in corpus (16)

• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
• Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A_{2n}^{(2)}),U_q(C_n^{(1)})$ and $U_q(D_{n+1}^{(2)})$
• An Ising-type formulation of the six-vertex model
• Matrix product solutions to the reflection equation from three dimensional integrability
• Integrable 3D lattice model in M-theory
• New solutions to the tetrahedron equation associated with quantized six-vertex models
• Solution of tetrahedron equation and cluster algebras
• Pentagon Relations in Direct Sums and Grassmann Algebras
• Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_q(D_{n+1}^{(2)}),U_q(A_{2n}^{(2)})$ and $U_q(C_n^{(1)})$
• Higher level $q$-oscillator representations for $U_q(C_n^{(1)}),U_q(C^{(2)}(n+1))$ and $U_q(B^{(1)}(0,n))$
• Tetrahedron equation and Schur functions
• Reflection $K$ matrices associated with an Onsager coideal of $U_p(A_{n-1}^{(1)})$, $U_p(B_n^{(1)})$, $U_p(D_n^{(1)})$ and $U_p(D_{n+1}^{(2)})$
• Tetrahedron equation and quantum $R$ matrices for $q$-oscillator representations
• Matrix product solutions to the $G_2$ reflection equation
• Combinatorial Yang-Baxter maps arising from tetrahedron equation