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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.


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I would recommend looking at Thurston's paper: In particular, he proves that the reps. preserve a certain quadratic form, which you might see being preserved by the Gassner rep. too. – Ian Agol Apr 28 '12 at 15:10
Thanks a lot. This paper looks very interesting. Regards, Aakumadula – Venkataramana Apr 29 '12 at 2:24
up vote 3 down vote accepted

See "Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation" 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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Thanks very much. This is most helpful. Regards, Aakumadula – Venkataramana Apr 29 '12 at 2:25

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