On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
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Ali Baklouti
,
Sonia Ghaouar
Abstract
Let ℍ2n+1r be the reduced Heisenberg Lie group, G = ℍ2n+1r × ℍ2n+1r be the (4n + 2)-dimensional Lie group and ΔG = {(x,x) ∈ G : x ∈ ℍ2n+1r} be the diagonal subgroup of G. Given any discontinuous subgroup Γ ⊂ G for G/ΔG, we provide a layering of the parameter space ℛ(Γ, G, ΔG), which is shown to be endowed with a smooth manifold structure, we also show that the stability property holds. On the other hand, a local (and hence a global) rigidity theorem is obtained. That is, the parameter space ℛ(Γ, G, ΔG) admits a rigid point if and only if Γ is finite and this is also equivalent to the fact that the deformation space is Hausdorff.
Funding source: D.G.R.S.R.T. Research Laboratory
Award Identifier / Grant number: LR 11ES52
The authors are deeply indebted to the referee for having suggested us many valuable comments to get the present form of the paper.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
- On the connectedness of the Chabauty space of a locally compact prosolvable group
- Holomorphically induced representations of exponential solvable semi-direct product groups ℝ ⋉ ℝn
- The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type A2
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
- On the connectedness of the Chabauty space of a locally compact prosolvable group
- Holomorphically induced representations of exponential solvable semi-direct product groups ℝ ⋉ ℝn
- The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type A2
