Quantum resonances and scattering poles of classical rank one locally symmetric spaces

2024/03/21 by Benjamin Delarue, Delarue, Benjamin, Joachim Hilgert +1
Mathematics · Physics and Astronomy · #22E46 #53C35 #58J50 #81U24 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2403.14426

openalex publication_date 2024/03/21 · openalex created_date 2024/03/24 · openalex updated_date 2026/07/28

Abstract

For negatively curved symmetric spaces it is known from [Hansen-Hilgert-Parthasarathy,2019] 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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