Abstract
Under a weight conservation condition when q is not a root of unity, Yang-Baxter relations are solved without the assumption that the upper-left triangle of each sub-block of the S matrix of the braid group representation (BGR) vanishes. A general form of BGR associated with Bn, Cn and Dn is obtained and shown to construct link invariants. The many-to-one correspondence between BGRs and link invariants is given.
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