Proc. Japan Acad. Ser. A Math. Sci. 96 (8), 69-74, (October 2020) DOI: 10.3792/pjaa.96.013
Fanny Kassel, Toshiyuki Kobayashi
KEYWORDS: locally symmetric space, pseudo-Riemannian manifold, discontinuous group, invariant differential operator, branching law, spherical variety, 22E40, 22E46, 58J50, 11F72, 53C35
We summarize and announce some recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or $\Gamma$ is trivial (e.g. Plancherel-type formula for semisimple symmetric spaces).