On the Determination of Irreducible Modules by Restriction to a Subalgebra

DOI10.2307/1996195zbMath0266.17014OpenAlexW3143996795MaRDI QIDQ5682931

G. W. McCollum, James Lepowsky

Publication date: 1973

Full work available at URL: https://doi.org/10.2307/1996195

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Universal enveloping (super)algebras (17B35) Infinite-dimensional Lie (super)algebras (17B65) Representation theory of associative rings and algebras (16Gxx)

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Cites Work

• Unnamed Item
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• On the existence and irreducibility of certain series of representations
• Algebraic Results on Representations of Semisimple Lie Groups
• A Theory of Spherical Functions. I
• Representations of a Semisimple Lie Group on a Banach Space. I
• Representations of semisimple Lie groups. II