Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups

DOI10.1016/J.JFA.2012.08.026zbMath1264.22011arXiv1203.5462OpenAlexW2166147337WikidataQ102464930 ScholiaQ102464930MaRDI QIDQ694761

Joachim Hilgert, Jan Möllers, Toshiyuki Kobayashi, Bent Orsted

Publication date: 13 December 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5462

zbMATH Keywords

spherical harmonicsBessel functionminimal representationJordan algebrabranching lawFock modelSchrödinger modelSegal-Bargmann transformHermitian Lie group

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Analysis on other specific Lie groups (43A80)

Related Items (8)

Minimal representations of simple real Lie groups of non Hermitian type ⋮ Classification of minimal representations of real simple Lie groups ⋮ A superunitary Fock model of the exceptional Lie supergroup \(\mathbb{D}(2, 1; \alpha)\) ⋮ A Schr\"odinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha)$ ⋮ A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(m, 2 | 2n)\) ⋮ Some genuine small representations of a nonlinear double cover ⋮ Segal-Bargmann transforms associated to a family of coupled supersymmetries ⋮ Analysis of minimal representations of \(\mathrm{SL}(n, \mathbb{R})\)

Cites Work

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• Remarks on real nilpotent orbits of a symmetric pair
• Segal-Bargmann transforms associated with finite Coxeter groups
• Laguerre functions on symmetric cones and recursion relations in the real case
• Segal-Bargmann and Weyl transforms on compact Lie groups
• Fonctions de Bessel sur une algèbre de Jordan. (Bessel functions on a Jordan algebra)
• Unitary representations defined by boundary conditions - the case of sl(2,R)
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• Discrete decomposability of the restriction of \(A_{{\mathfrak q}}(\lambda)\) with respect to reductive subgroups. III: Restriction of Harish-Chandra modules and associated varieties
• Analysis on the minimal representation of \(\mathrm O(p,q)\). II: Branching laws.
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Representations in \(L^{2}\)-spaces on infinite-dimensional symmetric cones
• Integral formulas for the minimal representation of \(O(p,2\))
• Analysis of the Brylinski-Kostant Model for Spherical Minimal Representations
• The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞)
• Laguerre semigroup and Dunkl operators
• Harmonic analysis of the de Rham complex on the sphere.
• The minimal orbit in a simple Lie algebra and its associated maximal ideal
• Minimal representations, geometric quantization, and unitarity.
• Representation theory and convexity

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