𝐿²(𝐺_{𝑄}\𝐺_{𝐴}) is not always multiplicity-free

Corwin, Lawrence

doi:10.1090/S0002-9939-1976-0399370-9

$L^{2}(G_{Q}\backslash G_{A})$ is not always multiplicity-free
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by Lawrence Corwin

Proc. Amer. Math. Soc. 56 (1976), 329-332

DOI: https://doi.org/10.1090/S0002-9939-1976-0399370-9

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Abstract:

We show that there are solvable adelic groups ${G_{\mathbf {A}}}$ whose action on ${L^2}({G_{\mathbf {Q}}}\backslash {G_{\mathbf {A}}}),{G_{\mathbf {Q}}}\backslash {G_{\mathbf {A}}}$ compact, it is not multiplicity-free.

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