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.
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Universität Paderborn, Institut für Mathematik, Germany
Benjamin Delarue; Joachim Hilgert. Quantum Resonances and Scattering Poles of Classical Rank One Locally Symmetric Spaces. Journal of Lie Theory, Tome 35 (2025) no. 4, pp. 787-804. http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a4/
@article{JOLT_2025_35_4_a4,
author = {Benjamin Delarue and Joachim Hilgert},
title = {Quantum {Resonances} and {Scattering} {Poles} of {Classical} {Rank} {One} {Locally} {Symmetric} {Spaces}},
journal = {Journal of Lie Theory},
pages = {787--804},
year = {2025},
volume = {35},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a4/}
}
TY - JOUR
AU - Benjamin Delarue
AU - Joachim Hilgert
TI - Quantum Resonances and Scattering Poles of Classical Rank One Locally Symmetric Spaces
JO - Journal of Lie Theory
PY - 2025
SP - 787
EP - 804
VL - 35
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a4/
ID - JOLT_2025_35_4_a4
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%T Quantum Resonances and Scattering Poles of Classical Rank One Locally Symmetric Spaces
%J Journal of Lie Theory
%D 2025
%P 787-804
%V 35
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a4/
%F JOLT_2025_35_4_a4
