Holomorphic representations of nilpotent Lie groups

DOI10.1016/0022-1236(79)90100-9zbMath0416.22013OpenAlexW2013136583MaRDI QIDQ754313

Roe Goodman

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0022-1236(79)90100-9

zbMATH Keywords

unitary representationsentire functionsintegral representationsgrowth propertiesreal formholomorphic representationcomplex nilpotent Lie group

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Complex Lie groups, group actions on complex spaces (32M05)

Related Items (3)

Conditions necessaires d'hypoanalyticite pour des opérateurs invariants à gauche homogenes sur un groupe nilpotent gradue ⋮ \(K\)-finite matrix elements of irreducible Harish-Chandra modules are hypergeometric functions ⋮ Arens–Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms

Cites Work

• Representations of differential operators on a Lie group
• Exponential operators from anharmonic oscillators
• Filtrations and asymptotic automorphisms on nilpotent Lie groups
• Hypoelliptic second order differential equations
• Some regularity theorems for operators in an enveloping algebra
• Intertwining operators for semisimple groups
• Sur quelques extensions de la notion de distribution
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• Croissance polynomiale et périodes des fonctions harmoniques
• Commutative subalgebra of 𝐿¹(𝐺) associated with a subelliptic operator on a Lie group 𝐺
• Filtrations and Canonical Coordinates on Nilpotent Lie Groups
• Analytic and Entire Vectors for Representations of Lie Groups
• Complex Fourier Analysis on a Nilpotent Lie Group
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