Return to Question

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. For an irreducible unitary representation $\pi$ of $G$ let $$ m_\Gamma(\pi)=\dim\mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ be its automorphic multiplicity. In [1], Chapter 3 one finds that $m_\Gamma(\pi)$ is finite if $G$ is a reductive Lie group and $\Gamma$ is arithmetic. The authors seem to indicate that there are examples when $m_\Gamma(\pi)=\infty$, but they don't give one.

Where can I find such an example? Are there examples with $G$ being a Lie group?

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. For an irreducible unitary representation $\pi$ of $G$ let $$ m_\Gamma(\pi)=\dim\mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ be its automorphic multiplicity. In [1], Chapter 3 one finds that $m_\Gamma(\pi)$ is finite if $G$ is a reductive Lie group and $\Gamma$ is arithmetic. The authors seem to indicate that there are examples when $m_\Gamma(\pi)=\infty$, but they don't give one.

Where can I find such an example? Are there examples with $G$ being a Lie group?

[1] Osborne, M. Scott; Warner, Garth: The theory of Eisenstein systems. Academic Press, New York-London, 1981.

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. For an irreducible unitary representation $\pi$ of $G$ let $$ m_\Gamma(\pi)=\dim\mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G) $$ be its automorphic multiplicity. In [1], Chapter 3 one finds that $m_\Gamma(\pi)$ is finite if $G$ is a reductive Lie group and $\Gamma$ is arithmetic. The authors seem to indicate that there are examples when $m_\Gamma(\pi)=\infty$, but they don't give one.

Where can I find such an example? Are there examples with $G$ being a Lie group?

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. For an irreducible unitary representation $\pi$ of $G$ let $$ m_\Gamma(\pi)=\dim\mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ be its automorphic multiplicity. In [1], Chapter 3 one finds that $m_\Gamma(\pi)$ is finite if $G$ is a reductive Lie group and $\Gamma$ is arithmetic. The authors seem to indicate that there are examples when $m_\Gamma(\pi)=\infty$, but they don't give one.

Where can I find such an example? Are there examples with $G$ being a Lie group?