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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 1, Pages 115–132 (Mi izv64)  

On $q$-monodromy groups of singularities

G. G. Ilyuta


Abstract: 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.

DOI: https://doi.org/10.4213/im64

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English version:
Izvestiya: Mathematics, 1996, 60:1, 119–136

Bibliographic databases:

MSC: 58C27
Received: 01.11.1994

Citation: G. G. Ilyuta, “On $q$-monodromy groups of singularities”, Izv. RAN. Ser. Mat., 60:1 (1996), 115–132; Izv. Math., 60:1 (1996), 119–136

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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