Finite orbits of the braid group action on sets of reflections

Details Finite orbits of the braid group action on sets of reflections Finite orbits of the braid group action on sets of reflections

2004-09-14

arxiv.org/abs/math-ph/0409026v4

Physics

Mathematical Physics

rewritten for clarity, 57 pages, 47 figures, LaTeX

Scientific paper

The finite orbits of the braid group action on Stokes matrices are studied and are shown to be the orbits on ordered sets of reflections, generating finite groups. All invariants of a reflection arrangement are determined. Determination of the orbits of the braid group on non-redundant generaing reflections in finite groups is done in a new way. The original idea is to introduce universal sets of generators in each group. These sets are found for all finite Coxeter groups. The orbits are classified for non-degenerate arrangement matrices.

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