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

Abstract

We consider quotients of the group algebra of the $3$-string braid group $B_3$ 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.

arXiv commentCompared to previous version the introduction and the List of references are extended, few remarks added