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arXiv · 1308.6473

Tetrahedron equation and quantum R matrices for infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2)

Atsuo Kuniba·Masato Okado
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Abstract

From the q-oscillator solution to the tetrahedron equation associated with a quantized coordinate ring, we construct solutions to the Yang-Baxter equation by applying a reduction procedure formulated earlier by S. Sergeev and the first author. The results are identified with the quantum R matrices for the infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2) corresponding to an affinization of Verma modules of their subalgebras isomorphic to U_q(sl_2) and U_{q^4}(sl_2).

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Atsuo Kuniba, Masato Okado. 2013-11-13. Tetrahedron equation and quantum R matrices for infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2). https://doi.org/10.1088/1751-8113/46/48/485203

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