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Tensor Product of Krammer’s Representations of the P<sub>3</sub>

Author(s): Hassan A. Tarraf | Mohammad N. Abdulrahim

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 02;
Issue: 03;
Start page: 190;
Date: 2012;
Original page

Keywords: Braid Group | Pure Braid Group | Magnus Representation | Krammer’s Representation

We consider the complex specializations of Krammer’s representation of the pure braid group on three strings, namely K(q,t), where q and t are non-zero complex numbers. We then specialize the indeterminate t by one and replace by for simplicity. Then we present our main theorem that gives us sufficient conditions that guarantee the irreducibility of the tensor product of two irreducible complex specializations of Krammer’s repre- sentations .
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