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Holomorphically induced representations of exponential solvable semi-direct product groups ℝ ⋉ ℝn
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Junko Inoue
Published/Copyright:
March 19, 2015
Abstract
Let G be an exponential solvable Lie group with Lie algebra 𝔤 defined by a semi-direct product of ℝ and ℝn. We study a holomorphically induced representation ρ of G from a real linear form f of 𝔤 and a 1-dimensional complex subalgebra 𝔥 of 𝔤ℂ such that the space 𝔥 + 𝔥̅ generates 𝔤ℂ. Under some assumptions of structure of the Lie algebra, we obtain a sufficient condition for non-triviality of ρ and decompose ρ into a multiplicity-free direct integral of irreducible representations.
Funding source: JSPS KAKENHI
Award Identifier / Grant number: 25400115
Received: 2015-10-22
Revised: 2014-12-21
Accepted: 2014-12-24
Published Online: 2015-3-19
Published in Print: 2015-4-1
© 2015 by De Gruyter
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- 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
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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
