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Complex specializations of the reduced Gassner representation of the pure braid group


Author: Mohammad N. Abdulrahim
Journal: Proc. Amer. Math. Soc. 125 (1997), 1617-1624
MSC (1991): Primary 20F36
DOI: https://doi.org/10.1090/S0002-9939-97-04081-1
MathSciNet review: 1422839
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Abstract: We will give a necessary and sufficient condition for the specialization of the reduced Gassner representation $G_{n}(z): P_{n} \to GL_{n-1}(\mathbb {C})$ to be irreducible. It will be shown that for $z=(z_{1},\ldots ,z_{n})\in (\mathbb {C}^{*})^{n}$, $G_{n}(z)$ is irreducible if and only if $z_{1}\ldots z_{n} \neq 1$.


References [Enhancements On Off] (What's this?)

  • [1] M. Abdulrahim, The Gassner Representation of the Pure Braid Group, Doctoral Thesis, The Pennsylvania State University, 1995.
  • [2] J.S. Birman, Braids, Links and Mapping Class Groups, Vol 82 of Annals of Mathematical Studies, Princeton University Press, New Jersy, 1975. MR 51:11477; MR 54:13894
  • [3] L. Dornhoff, Group Representation Theory, Part A, Marcel Dekker Inc., New York, 1971. MR 50:458a
  • [4] E. Formanek, Braid group representations of low degree, Proc. London Math. Soc. 73 (1996), 279-322. CMP 96:15
  • [5] V.L. Hansen, Braids and Coverings, London Mathematical Society. Cambridge University Press, 1989. MR 94g:57004

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Additional Information

Mohammad N. Abdulrahim
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: mna@math.psu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-04081-1
Keywords: Braid group, pure braid group, Burau representation, Gassner representation
Received by editor(s): December 23, 1995
Additional Notes: The results in this paper were written under the direction of Professor Edward Formanek whose help and encouragement are greatly appreciated.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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