Conformally invariant systems of differential equations and prehomogeneous vector spaces of Heisenberg parabolic type

DOI10.2977/prims/1216238304zbMath1196.22011OpenAlexW2016501154MaRDI QIDQ2518196

Leticia Barchini, Anthony C. Kable, Roger Zierau

Publication date: 15 January 2009

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1216238304

zbMATH Keywords

generalized Verma modulesGyoja's conjecturecovariant maps

Mathematics Subject Classification ID

Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (13)

Special values for conformally invariant systems associated to maximal parabolics of quasi-Heisenberg type ⋮ On the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras ⋮ Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type ⋮ Algebraic analysis of scalar generalized Verma modules of Heisenberg parabolic type I: \(\mathsf{A}_{n}\)-series ⋮ Reducibility of generalized Verma modules for Hermitian symmetric pairs ⋮ Heisenberg parabolically induced representations of Hermitian Lie groups, part I: Intertwining operators and Weyl transform ⋮ The Dynkin index and conformally invariant systems associated to parabolic subalgebras of Heisenberg type ⋮ Unnamed Item ⋮ Mathews' Identity for Prehomogeneous Vector Spaces of Heisenberg Parabolic Type ⋮ Conformally invariant systems of differential operators ⋮ \(K\)-finite solutions to conformally invariant systems of differential equations ⋮ On the space of 𝐾-finite solutions to intertwining differential operators ⋮ Leading weight vectors and homomorphisms between generalized Verma modules

Cites Work

• A duality theorem for extensions of induced highest weight modules
• Conformally invariant systems of differential operators
• Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren
• Intertwining differential operators and reducibility of generalized Verma modules
• Basic covariant differential operators on hermitian symmetric spaces
• Theb-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces
• Lie groups beyond an introduction
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