Realization of quaternionic discrete series on the unit ball in \(\mathbb H^d\)

DOI10.1016/j.jfa.2011.12.019zbMath1241.22008OpenAlexW2061869039MaRDI QIDQ408133

Genkai Zhang, He Ping Liu

Publication date: 29 March 2012

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.12.019

zbMATH Keywords

symmetric spacesLie groupscohomology spacesreproducing kernelsquaternionic discrete seriesSchmid's Dirac operator

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) General properties and structure of real Lie groups (22E15)

Related Items (6)

On the Hodge-type decomposition and cohomology groups of \(k\)-Cauchy-Fueter complexes over domains in the quaternionic space ⋮ Branching problems in reproducing kernel spaces ⋮ \(L^p\) joint eigenfunction bounds on quaternionic spheres ⋮ Integrability of quaternion-Kähler symmetric spaces ⋮ The Plancherel formula of Fourier integral operators: The case of Sp(1,1) ⋮ Sub-Riemannian Geometry and Hypoelliptic Operators

Cites Work

• Fourier-Jacobi expansion of automorphic forms on \(\text{Sp}(1,q)\) generating quaternionic discrete series
• Theta lifting from elliptic cusp forms to automorphic forms on \(\mathrm{Sp}(1, q)\)
• Quaternionic analysis, representation theory and physics
• Quasi-conformal actions, quaternionic discrete series and twistors: \(\text{SU}(2, 1)\) and \(\text{G} _{2(2)}\)
• Szegoe kernels associated with discrete series
• Function spaces and reproducing kernels on bounded symmetric domains
• Quaternionic discrete series for $Sp(1,1)$
• On quaternionic discrete series representations, and their continuations.
• Linear field equations on self-dual spaces
• Singular unitary representations and discrete series for indefinite Stiefel manifolds 𝑈(𝑝,𝑞;𝐹)/𝑈(𝑝-𝑚,𝑞;𝐹)
• Composition Series and Intertwining Operators for the Spherical Principal Series. I
• Quaternionic analysis
• Sur les représentations unitaires des groupes de Lorentz généralisés
• On the existence and irreducibility of certain series of representations
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