A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(m, 2 | 2n)\)

DOI10.3842/SIGMA.2020.085zbMath1484.17014arXiv2002.12836OpenAlexW3008244208MaRDI QIDQ2217962

Sam Claerebout, Hendrik De Bie, Sigiswald Barbier

Publication date: 12 January 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.12836

zbMATH Keywords

spherical harmonicsLie superalgebrasminimal representationsFock modelSchrödinger modelSegal-Bargmann transformBessel-Fischer product

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46) Analysis on supermanifolds or graded manifolds (58C50) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (4)

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 \(\mathfrak{osp}(m, 2 | 2n)\) ⋮ Segal-Bargmann transforms associated to a family of coupled supersymmetries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Special functions associated with a certain fourth-order differential equation
• Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
• Unitary representations of nilpotent super Lie groups
• Analysis on the minimal representation of \(O(p,q)\). I: Realization via conformal geometry.
• 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 \(\mathbb{R}^{p-1,q-1}\)
• A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(m, 2 | 2n)\)
• Minimal representations via Bessel operators
• Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles
• Lie Supergroups, Unitary Representations, and Invariant Cones
• The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞)
• On a Hilbert space of analytic functions and an associated integral transform part I
• Fischer decomposition for polynomials on superspace
• Harmonic Analysis in Phase Space. (AM-122)
• A higher rank Racah algebra and the $\mathbb{Z}_2^n$ Laplace–Dunkl operator
• Polynomial Realisations of Lie (Super)Algebras and Bessel Operators
• Fréchet Globalisations of Harish-Chandra Supermodules
• On structure and TKK algebras for Jordan superalgebras
• The orthosymplectic superalgebra in harmonic analysis
• A Minimal Representation of the Orthosymplectic Lie Supergroup
• Superunitary Representations of Heisenberg Supergroups
• Orthosymplectically invariant functions in superspace
• Spherical harmonics and integration in superspace
• Super unitary representations revisited

This page was built for publication: A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(m, 2 | 2n)\)