Journal of Lie Theory 35 (2025), No. 4, 787--804
Copyright Heldermann Verlag 2025
Quantum Resonances and Scattering Poles of Classical Rank One Locally Symmetric Spaces
Benjamin Delarue
Universität Paderborn, Institut für Mathematik, Germany
bdelarue@math.upb.de
Joachim Hilgert
Universität Paderborn, Institut für Mathematik, Germany
hilgert@math.upb.de
For negatively curved symmetric spaces it is known from S. Hansen, J. Hilgert, and A. Parthasarathy [Resonances and scattering poles in symmetric spaces of rank one, Int. Math. Res. Notices 20 (2019) 6362--6389] that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms.
Keywords: Scattering theory, meromorphic continuation, Laplace operator.
MSC: 53C35, 58J50, 81U24, 22E46.
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