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arXiv · 1411.2213

Tetrahedron equation and quantum $R$ matrices for $q$-oscillator representations

Atsuo Kuniba·Masato Okado
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Abstract

We review and supplement the recent result by the authors on the reduction of the three dimensional $R$ (3d $R$) satisfying the tetrahedron equation to the quantum $R$ matrices for the $q$-oscillator representations of $U_q(D^{(2)}_{n+1})$, $U_q(A^{(2)}_{2n})$ and $U_q(C^{(1)}_{n})$. A new formula for the 3d $R$ and a quantum $R$ matrix for $n=1$ are presented and a proof of the irreducibility of the tensor product of the $q$-oscillator representations is detailed.

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Atsuo Kuniba, Masato Okado. 2014-11-09. Tetrahedron equation and quantum $R$ matrices for $q$-oscillator representations. https://doi.org/10.1088/1742-6596%2F597%2F1%2F012051

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