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Solutions to the Yang-Baxter Equation for the Spinor Representations of q-De
Boyuan HOU, Zhongqi RIA
Communications in Theoretical Physics
1991, 16 (2):
179-194.
In this paper, both trigonometric and rational solutions to tlre Yang-Baxter equation associated with the spinor representations of the quantum Dl univcrsal enveloping algebras are obtained. The quantum Clebsch-Gordan matrices, the quantum projectors and the solutions are the block matrices with the dimensions of tire submatrices to Le 1 and 2n-3 , 1l', where l' = l/2 + 1, if l' is even, l' = (l + 1)/2, if l is odd. Tlre csplicit forms of the submatrices with the same dimensions are indcpendcrlt of l. As esamples, we discuss the solutions for the spinor representations of the quantum D4 to D7, and prcscnt tlre explicit forms of those submatrices with the dimensions 1, 2, 8 and 32. Tlre corresponding representations of the braid group and the link polynomials are also computed tlrrougll a standard method.
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