The structure of the space of polynomial solutions to the canonical central systems of differential equations on the block Heisenberg groups: a generalization of a theorem of Korányi

DOI10.2748/tmj/1546570824zbMath1410.35268OpenAlexW2907817210MaRDI QIDQ1732296

Anthony C. Kable

Publication date: 22 March 2019

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tmj/1546570824

zbMATH Keywords

Heisenberg Laplacianconformally invariant systemdual \(b\)-function identitymodule of polynomial solutions

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Polynomial solutions to PDEs (35C11)

Related Items (2)

Deficient homomorphisms between generalized Verma modules ⋮ Polynomial and horizontally polynomial functions on Lie groups

Cites Work

• On certain conformally invariant systems of differential equations
• On certain conformally invariant systems of differential equations. II: Further study of type A systems
• Highest weight modules associated with classical irreducible regular prehomogeneous vector spaces of commutative parabolic type
• The Heisenberg ultrahyperbolic equation: \(K\)-finite and polynomial solutions
• Two Notes on Notation
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group

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