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Working paper

Representations of finite-dimensional quotient algebras of the 3-string braid group

We consider quotients of the group algebra of the 3-string braid group B3 by p-th order generic polynomial relations on the elementary braids. In cases p=2,3,4,5 these quotient algebras are finite dimensional. We give semisimplicity criteria for these algebras and present explicit formulas for all their irreducible representations.