Tetrahedron equation and quantum R matrices for q-oscillator representations
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 Uq(D(2)n+1), Uq(A(2)2n) and Uq(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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