A New Six Dimensional Representation of the Braid Group on Three Strands and its Irreducibility and Unitarizability
Madline A. Al-Tahan
Department of Mathematics, Beirut Arab University, Lebanon
Mohammad N. Abdulrahim *
Department of Mathematics, Beirut Arab University, Lebanon
*Author to whom correspondence should be addressed.
Abstract
We consider the braid group on three strands, B3and construct a complex valued representation of it with degree 6, namely, 
First, we show that this representation is irreducible and not equivalent to either Burau or Krammer’s representations. Second, we prove that the representation is unitary relative to an invertible hermitian matrix.
Keywords: Krammer’s representation, Artin representation, braid group, Hecke algebra