Abstract
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 .
Highlights
Let Bn be the braid group on n strings
Aut Fn sometimes gives rise to linear representations of Bn and its normal subgroup, the pure braid group denoted by Pn
We considered Krammer’s representations of B3 and P3 and we specialized the indeterminates to non zero complex numbers
Summary
Let Bn be the braid group on n strings. It has many kinds of linear representations. Note that in a previous work of Abdulrahim and Al-Tahan [2], a necessary and sufficient condition for the irreducibility of Krammer’s representation of degree three was found. In this way, we will have succeeded in constructing a representation of the pure braid group, P3, of degree nine and which is irreducible
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