Notes on affine isometric actions of discrete groups

Abstract

Consider a lattice $\Gamma$ in a group $G=S{L}_2(\mathbb{R}),SO(1,n),SU(1,n)$, $SL_2(\Q_p)$. We discuss actions of $\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its restriction to $\Gamma$ is irreducible. We prove the existence of canonical irreducible affine isometric actions of $\Gamma$ associated to actions of $\Gamma$ on $\mathbb{R}$- trees. Using such actions we construct irreducible representations of semigroup of probabilistic measures on $\Gamma$ and construct the series of representations of the groups of diffeomorphisms of Riemann surfaces enumerated by the points of Thurston compactification of Teichmüller (Teichmuller) space.

LaTeX2e, 47 pages

Cited by in corpus (1)

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