Quantum Resonances and Scattering Poles of Classical Rank One Locally Symmetric Spaces
Journal of Lie Theory, Volume 35 (2025) no. 4, pp. 787-804
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.
DOI:
10.5802/jolt.1408
Classification:
53C35, 58J50, 81U24, 22E46
Keywords: Scattering theory, meromorphic continuation, Laplace operator
Keywords: Scattering theory, meromorphic continuation, Laplace operator
@article{JOLT_2025_35_4_a4,
author = {B. Delarue and J. 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},
doi = {10.5802/jolt.1408},
zbl = {08124771},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1408/}
}
TY - JOUR AU - B. Delarue AU - J. 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 - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1408/ DO - 10.5802/jolt.1408 ID - JOLT_2025_35_4_a4 ER -
B. Delarue; J. Hilgert. Quantum Resonances and Scattering Poles of Classical Rank One Locally Symmetric Spaces. Journal of Lie Theory, Volume 35 (2025) no. 4, pp. 787-804. doi: 10.5802/jolt.1408
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