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I am looking for a specific reference to the connection between [1] the Deligne-Mostow monodromy and [2] Gassner representation at roots of unity of the pure braid group. I have seen many references but no specific place where this is established.

Any help will be most appreciated.

Aakumadula

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  • $\begingroup$ I would recommend looking at Thurston's paper: msp.warwick.ac.uk/gtm/1998/01/p025.xhtml In particular, he proves that the reps. preserve a certain quadratic form, which you might see being preserved by the Gassner rep. too. $\endgroup$
    – Ian Agol
    Commented Apr 28, 2012 at 15:10
  • $\begingroup$ Thanks a lot. This paper looks very interesting. Regards, Aakumadula $\endgroup$
    – Venkataramana
    Commented Apr 29, 2012 at 2:24

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See

  • Michael Kapovich, John J. Millson, Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation, Canadian Mathematical Bulletin, 44(1) (2001) 36-60, doi:10.4153/CMB-2001-006-3, arXiv:math/0002222

for the explicit relation between representations constructed via hypergeometric integrals and Gassner. We also explain the connection to [DM]. The representations we construct in the paper are mildly different from the ones in [DM], but you just have to replace our parameters $\epsilon_j=\pm 1$ with $\sqrt{-1}$ (to get [DM]).

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  • $\begingroup$ Thanks very much. This is most helpful. Regards, Aakumadula $\endgroup$
    – Venkataramana
    Commented Apr 29, 2012 at 2:25

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