Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A^{(2)}_{2n}), U_q(C^{(1)}_{n})$ and $U_q(D^{(2)}_{n+1})$

Published 18 Nov 2013 in math-ph, math.MP, math.QA, and nlin.SI | (1311.4258v3)

Abstract: The intertwiner of the quantized coordinate ring $A_q(sl_3)$ is known to yield a solution to the tetrahedron equation. By evaluating their $n$-fold composition with special boundary vectors we generate series of solutions to the Yang-Baxter equation. Finding their origin in conventional quantum group theory is a clue to the link between two and three dimensional integrable systems. We identify them with the quantum $R$ matrices associated with the $q$-oscillator representations of $U_q(A^{{(2)}_{2n})$,} $U_q(C^{(1)}_n)$ and $U_q(D^{{(2)}_{n+1})$.}