Boundary unitary representations-irreducibility and rigidity
Copyright policy )Boundary unitary representations-irreducibility and rigidity
Let $M$ be compact negatively curved manifold, $Γ=π_1(M)$ and $\tilde{M}$ be its universal cover. Denote by $B =\partial \tilde{M}$ the geodesic boundary of $\tilde{M}$ and by $ν$ the Patterson-Sullivan measure on $X$. In this note we prove that the associated unitary representation of $Γ$ on $L^2(B,ν)$ is irreducible. We also establish a new rigidity phenomenon: we show that some of the geometry of $M$, namely its marked length spectrum, is reflected in this $L^2$-representations.
- Muchnik Roman G United States
General theory of von Neumann algebras, orbits, Dynamical Systems (math.DS), Group Theory (math.GR), fundamental group, unitary representations, von Neumann algebra, group actions, topological dynamics, FOS: Mathematics, group algebra, Mathematics - Dynamical Systems, Representation Theory (math.RT), Projective representations and multipliers, Ergodic theory of linear operators, Banach space, Riemannian manifold, Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.), Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, predual, 37, 20, negative sectional curvature, Radon-Nikodým density, quasiregular representation, Geometric group theory, Mathematics - Group Theory, Mathematics - Representation Theory, geodesics
General theory of von Neumann algebras, orbits, Dynamical Systems (math.DS), Group Theory (math.GR), fundamental group, unitary representations, von Neumann algebra, group actions, topological dynamics, FOS: Mathematics, group algebra, Mathematics - Dynamical Systems, Representation Theory (math.RT), Projective representations and multipliers, Ergodic theory of linear operators, Banach space, Riemannian manifold, Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.), Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, predual, 37, 20, negative sectional curvature, Radon-Nikodým density, quasiregular representation, Geometric group theory, Mathematics - Group Theory, Mathematics - Representation Theory, geodesics
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