On the Faithfulness of the Representations of the Extraspecial 2-Groups E-1m.

We consider a family of representations of the braid groups Bn corresponding to a specific solution to the Yang-Baxter equation. The images of the pure braid group Pn, a normal subgroup of Bn, under these representations are extraspecial 2-groups and the images of the braid group Bn are extensions of extraspecial 2-groups. We determine conditions under which any representation of the extraspecial 2-group, Em-1, is faithful. We then show that the irreducible representations of Em-1, constructed by Franko, Rowell and Wang, are faithful if and only if m = 2k or m = 2k - 1 (k odd); where as it is not faithful if m = 2k - 1 (k even). [ABSTRACT FROM AUTHOR]