ON THE IRREDUCIBLITY OF THE REPRESENTATION OF
THE PURE BRAID GROUP ON THREE STRANDS
Hasan A. Haidar1, Mohammad N. Abdulrahim2
1,2Department of Mathematics
Beirut Arab University
P.O. Box 11-5020, Beirut, LEBANON

Abstract

Consider a representation $\rho:B_{3}\rightarrow GL_{6}(\mathbb{C})$ constructed by M. Al-Tahan and M. Abdulrahim. We construct a representation $\phi$ equivalent to the restriction of $\rho$ on $P_{3}$ and show that $\phi$ is a direct sum of irreducible subrepresentations, which are not equivalent to the reduced Burau representation restricted to $P_{3}$. Also, we show that the subrepresentations of $\phi$ are unitary relative to unique invertible hermitian matrices.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 2
Year: 2019

DOI: 10.12732/ijam.v32i2.7

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