Integral formula of the unitary inversion operator for the minimal representation of \(\text{O}(p,q)\)

DOI10.3792/pjaa.83.27zbMath1230.22007arXivmath/0607007OpenAlexW2076081575MaRDI QIDQ2381153

Gen Mano, Toshiyuki Kobayashi

Publication date: 25 September 2007

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607007

zbMATH Keywords

Weil representationSchrödinger modelindefinite orthogonal groupMinimal unitary representation

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Analysis on other specific Lie groups (43A80)

Related Items (10)

Generalized Bernstein-Reznikov integrals ⋮ Orthogonal polynomials associated to a certain fourth order differential equation ⋮ Geometric analysis on small unitary representations of \(\text{GL}(N, \mathbb R)\) ⋮ Special functions associated with a certain fourth-order differential equation ⋮ Minimal representations via Bessel operators ⋮ Integral formulas for the minimal representation of \(O(p,2\)) ⋮ Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform ⋮ The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞) ⋮ An integral formula forL²-eigenfunctions of a fourth-order Bessel-type differential operator ⋮ Laguerre semigroup and Dunkl operators

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