2000 character limit reached
Tetrahedron equation and quantum $R$ matrices for $q$-oscillator representations (1411.2213v1)
Published 9 Nov 2014 in math-ph, math.MP, math.QA, and nlin.SI
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.