Abstract
A weight conservation condition for the S-matrix of the braid group representation, from which non-vanishing elements of the S-matrix can be determined, is introduced. A method of weight lattice analysis of representations of Lie algebra is suggested and used to give structures of braid group representations in various cases. This makes it feasible for braid group representations to be obtained by solving the spectral parameter independent Yang-Baxter equation directly, which leads to several new braid group representations.
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