Geodesic
On some Finite-Dimensional Representations of Artin Braid Group
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 33-41.

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The author studies certain homomorphic images G of the Artin braid group on n strands in finite symmetric groups. Any permutation group G is an extension of the symmetric group on n letters by an appropriate abelian group. The extension G depends on an integer parameter q ≥ 1, and splits if and only if 4 does not divide q. In the case when q is odd, all finite-dimensional irreducible representations of G are found, thus finding an infinite series of irreducible representations of the braid group. *2000 Mathematics Subject Classification: 20C15, 20C35, 20F36.
Keywords: Artin Braid Group, Permutation Representation, Split Extension, Finite-Dimensional, Irreducible Representation 
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Iliev, Valentin. On some Finite-Dimensional Representations of Artin Braid Group. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 33-41. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a0/