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arXiv · 1102.3036

Boundary unitary representations - irreducibility and rigidity

Uri Bader·Roman Muchnik
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Abstract

Let $M$ be compact negatively curved manifold, $\Gamma =\pi_1(M)$ and $\tilde{M}$ be its universal cover. Denote by $B =\partial \tilde{M}$ the geodesic boundary of $\tilde{M}$ and by $\nu$ the Patterson-Sullivan measure on $X$. In this note we prove that the associated unitary representation of $\Gamma$ on $L^2(B,\nu)$ 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.

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Uri Bader, Roman Muchnik. 2011-02-15. Boundary unitary representations - irreducibility and rigidity. https://arxiv.org/abs/1102.3036

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