Integral formulas for the minimal representation of \(O(p,2\))

DOI10.1007/s10440-005-0464-2zbMath1100.22007OpenAlexW2026825595MaRDI QIDQ2501313

Gen Mano, Toshiyuki Kobayashi

Publication date: 4 September 2006

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-005-0464-2

zbMATH Keywords

semigroup of operatorsWeil representationSchrödinger modelminimal unitary representationFourier--Bessel transform

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Analysis on other specific Lie groups (43A80)

Related Items (13)

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Cites Work

• Unnamed Item
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• Explicit Hilbert spaces for certain unipotent representations
• Kirillov-Duflo orbit method and minimal representations of simple groups over a local field of characteristic zero
• Analysis on the minimal representation of \(O(p,q)\). I: Realization via conformal geometry.
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Explicit Hilbert spaces for certain unipotent representations. II
• Unitarization of a singular representation of \(\text{SO}(p,q)\)
• Integral formula of the unitary inversion operator for the minimal representation of \(\text{O}(p,q)\)
• Harmonic Analysis in Phase Space. (AM-122)

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