On the space of 𝐾-finite solutions to intertwining differential operators

DOI10.1090/ERT/527zbMath1428.22014arXiv1808.10042OpenAlexW2972534125MaRDI QIDQ5240203

Toshihisa Kubo, Bent Orsted

Publication date: 24 October 2019

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.10042

zbMATH Keywords

duality theoremhypergeometric polynomialsgeneralized Verma modulessmall representationsintertwining differential operatorsK-finite solutionsPeter-Weyl-type formulasTorasso's representation

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46)

Cites Work

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• Differential symmetry breaking operators. I: General theory and F-method
• The Heisenberg ultrahyperbolic equation: the basic solutions as distributions
• A system of third-order differential operators conformally invariant under \(\mathfrak {sl}(3,\mathbb C)\) and \(\mathfrak {so}(8,\mathbb C)\)
• \(K\)-finite solutions to conformally invariant systems of differential equations
• A duality theorem for extensions of induced highest weight modules
• Conformally invariant systems of differential operators
• 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 \(\mathbb{R}^{p-1,q-1}\)
• Unitarization of a singular representation of \(\text{SO}(p,q)\)
• The Heisenberg ultrahyperbolic equation: \(K\)-finite and polynomial solutions
• Equivariant first order differential operators on boundaries of symmetric spaces
• Global representations of the conformal group and eigenspaces of the Yamabe operator on \(S^1 \times S^n\)
• Representations of \(\text{SU}(p,q)\) and CR geometry. I
• Conformally invariant systems of differential equations and prehomogeneous vector spaces of Heisenberg parabolic type
• Structure of representations generated by vectors of highest weight
• The minimal representation of the conformal group and classic solutions to the wave equation
• Small unitary representations of the double cover of $\operatorname{SL}(m)$
• The unitary irreducible representations of SL¯ (3,R)
• Uniqueness of Embeddings of Certain Induced Modules
• A Singular Representation of E 6
• Resonances for the Laplacian on Riemannian symmetric spaces: The case of 𝑆𝐿(3,ℝ)/𝕊𝕆(3)
• Some genuine small representations of a nonlinear double cover
• On Representations Associated to the Minimal Nilpotent Coadjoint Orbit of SL (3, R)
• Global representations of the Heat and Schr\"odinger equation with singular potential
• Structure of certain induced representations of complex semisimple Lie algebras

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