Geodesic
On $q$-monodromy groups of singularities
Izvestiya. Mathematics , Tome 60 (1996) no. 1, pp. 119-136

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In this paper some facts are proved concerning the $q$-analogue of symmetric and skew-symmetric monodromy groups of singularities. The image of the Burau representation of the group of braids on three strings is described. For $q$ a root of 1 the image of the group of $q$-coloured braids of a singularity in the skew-symmetric monodromy group is studied. The latter is distinguished among the $q$-monodromy groups for the roots of 1. The orbits of the braid monodromy group over $\mathbb Z$ are described. A connection is established between the spectra of the generalized Cartan $q$-matrix and the Coxeter $q$-operator for Coxeter–Dynkin diagrams without cycles of odd length. 
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     author = {G. G. Ilyuta},
     title = {On $q$-monodromy groups of singularities},
     journal = {Izvestiya. Mathematics },
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     number = {1},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_1_a4/}
}
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G. G. Ilyuta. On $q$-monodromy groups of singularities. Izvestiya. Mathematics , Tome 60 (1996) no. 1, pp. 119-136. http://geodesic.mathdoc.fr/item/IM2_1996_60_1_a4/