Braids and Permutations

By Vladimir Lin. 2004

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E. Artin described all irreducible representations of the braid group B_k to the symmetric group S(k). We strengthen some of his results and, moreover, exhibit a complete picture of homomorphisms of B_k to S(n) for n 6 there exist, up to conjugation, exactly 3 irreducible representations of B_k into S(2k) with non-cyclic images but they all are imprimitive. We use these results to prove that for n 4 the intersection PB_k\cap B'_k of PB_k with the commutator subgroup B'_k=[B_k,B_k] is a completely characteristic subgroup of B'_k.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ccc1d4176ad710daad017d29c9a6c102e5d74db9