Displaying similar documents to “Painlevé equations and complex reflections”

On the dynamics of (left) orderable groups

Andrés Navas (2010)

Annales de l’institut Fourier

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We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the...

Linear actions of free groups

Mark Pollicott, Richard Sharp (2001)

Annales de l’institut Fourier

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In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.

Monodromy representations of braid groups and Yang-Baxter equations

Toshitake Kohno (1987)

Annales de l'institut Fourier

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Motivated by the two dimensional conformal field theory with gauge symmetry, we shall study the monodromy of the integrable connections associated with the simple Lie algebras. This gives a series of linear representations of the braid group whose explicit form is described by solutions of the quantum Yang-Baxter equation.