Abstract
It is shown that from each self-dual representation of a quantum supergroup with nonvanishing q-superdimension, a graded representation of the Temperley–Lieb algebra can be constructed, which, in turn, gives rise to a solution of the graded Yang–Baxter equation. As examples, the vector irrep of Uq (osp(M/2n)) and all the finite-dimensional irreps of Uq (osp(1/2)) are studied, and the corresponding graded Ř-matrices are obtained explicitly. A general method is also given to obtain link polynomials from graded Ř-matrices. Applied to the ones associated with graded representations of the Temperley–Lieb algebra, the method yields the Jones polynomial.
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