Multi-parameter Burau representations
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Abstract
We consider the multi-parameter representation of Artin's braid group introduced by D. D. Long and J. P. Tian, namely $\alpha: B_{n}\rightarrow GL_{m}(C)$, where $m=n!n$ . First, we show that there exists a complex specialization of the multi-parameter representation that does not arise from any Hecke algebra. Second, we find conditions under which the images of the generators of the braid group on three strings under the multi-parameter representation are unitary relative to a nonsingular hermitian matrix.
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Abdulrahim, M. N., Tahan, M. A.-., & Habre, S. S. (2013). Multi-parameter Burau representations. Tamkang Journal of Mathematics, 44(1), 91–98. https://doi.org/10.5556/j.tkjm.44.2013.1081
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References
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