A superunitary Fock model of the exceptional Lie supergroup \(\mathbb{D}(2, 1; \alpha)\)

DOI10.1007/s00220-023-04793-8arXiv2301.07982OpenAlexW4386365549MaRDI QIDQ6046985

Sigiswald Barbier, Sam Claerebout

Publication date: 6 October 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.07982

Mathematics Subject Classification ID

Lie algebras and Lie superalgebras (17Bxx) Lie groups (22Exx) General theory of differentiable manifolds (58Axx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• 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 \(\mathrm O(p,q)\). II: Branching laws.
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Explicit Hilbert spaces for certain unipotent representations. II
• 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
• Mathematical foundations of supersymmetry
• 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)
• The Super Orbit Challenge
• Minimal representations, geometric quantization, and unitarity.
• Polynomial Realisations of Lie (Super)Algebras and Bessel Operators
• Fréchet Globalisations of Harish-Chandra Supermodules
• A Minimal Representation of the Orthosymplectic Lie Supergroup
• Superunitary Representations of Heisenberg Supergroups
• A Schr\"odinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha)$
• Super unitary representations revisited

This page was built for publication: A superunitary Fock model of the exceptional Lie supergroup \(\mathbb{D}(2, 1; \alpha)\)