Bulg. J. Phys. vol.33 no.s2 (2006), pp. 58-67


Braid Group Action and Symmetric Bases of Root Systems

A. Stefanov
Institute for Nuclear Research and Nuclear Energy, 72 Tzarigradsko Chaussee, BG-1784 Sofia, Bulgaria
Abstract. The braid groups can be realized as subgroups of the automorphism groups of free groups. This gives rise to an action of the braid groups on generators of arbitrary groups known as the Hurwitz action. This action on sets of reflections is discussed and a combinatorial approach to the classification of the finite orbits is presented. The most symmetric sets of reflections generating finite groups are introduced.

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