Concrete L²-spectral Analysis of a Bi-weighted Γ-automorphic Twisted Laplacian

We consider a twisted Laplacian Δ ν,μ on the n-complex space associated with the sub-Laplacian of the Heisenberg group ℂ ×ω ℂ n realized as a central extension of the real Heisenberg group H2n+1. The main results to which is aimed this paper concern the spectral theory of Δ ν , μ Γ when acting on so...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2021-10, Vol.25 (5), p.887-904
Main Authors: El Fardi, Aymane, Ghanmi, Allal, Intissar, Ahmed
Format: Article
Language:English
Online Access:Get full text
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Summary:We consider a twisted Laplacian Δ ν,μ on the n-complex space associated with the sub-Laplacian of the Heisenberg group ℂ ×ω ℂ n realized as a central extension of the real Heisenberg group H2n+1. The main results to which is aimed this paper concern the spectral theory of Δ ν , μ Γ when acting on some L² space of Γ-automorphic functions of biweight (ν, μ) associated to given cocompat discrete subgroup of the additive group ℂ n . We describe its spectrum proving a stability theorem. Using the Selberg’s approach, we give the explicit dimension formula for the corresponding L²-eigenspaces. We also construct a concrete basis of such L²-eigenspaces.
ISSN:1027-5487
2224-6851