Irreducibility of the Tensor Product of Specializations of the Burau Representation of the Braid Groups

الملخص EN

The reduced Burau representation is a one-parameter representation of Bn, the braid group on n strings.

Specializing the parameter to nonzero complex number x gives a representation βn(x): Bn→GL(ℂn−1), which is either irreducible or has an irreducible composition factor β^n(x): Bn→GL(ℂn−2).

In our paper, we let k≥2, and we determine a sufficient condition for the irreducibility of the tensor product of k irreducible Burau representations.

This is a generalization of our previous work concerning the cases k=2 and k=3.