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arXiv · 1311.4258

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

Atsuo Kuniba·Masato Okado
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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 $U_q(D^{(2)}_{n+1})$.

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Atsuo Kuniba, Masato Okado. 2014-04-21. Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A^{(2)}_{2n}), U_q(C^{(1)}_{n})$ and $U_q(D^{(2)}_{n+1})$. https://doi.org/10.1007/s00220-014-2147-1

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