On the centralizer of \(K\) in the universal enveloping algebra of \(\text{SO}(n,1)\) and \(\text{SU}(n,1)\)

DOI10.1007/BF02568189zbMath0813.22005OpenAlexW4241853547MaRDI QIDQ1343709

Juan Alfredo Tirao

Publication date: 30 January 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156013

zbMATH Keywords

Verma modulesintertwining operatorsintertwining relationsprincipal series representationsreal semisimple Lie groupIwasawa decompositionmaximal compact subgroupinjective anti-homomorphism

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Semisimple Lie groups and their representations (22E46)

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Cites Work

• A transversality property of a derivation of the universal enveloping algebra \(U(k)\), for \(SO(n,1)\) and \(SU(n,1)\)
• On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra
• Structure of representations generated by vectors of highest weight
• A Restriction Theorem for Semisimple Lie Groups of Rank One
• A Restriction Theorem for Modules Having a Spherical Submodule
• On the Structure of Certain Subalgebras of a Universal Enveloping Algebra
• Intégrales d'entrelacement et fonctions de Whittaker
• Orbits and Representations Associated with Symmetric Spaces
• Algebraic Results on Representations of Semisimple Lie Groups
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