Tetrahedron equation and quantum R matrices for infinite dimensional modules of Uq(A(1)1) and Uq(A(2)2)
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 Uq(A(1)1) and Uq(A(2)2) corresponding to an affinization of Verma modules of their subalgebras isomorphic to Uq(sl2) and Uq4(sl2).
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