Infinitesimal operators and structure of the most degenerate representations of the groups Sp( p+q) and Sp( p, q) in an Sp( p)×Sp(q) basis

DOI10.1063/1.526261zbMath0548.22009OpenAlexW2093498402MaRDI QIDQ3341063

Bruno Gruber, A. U. Klimyk

Publication date: 1984

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.526261

zbMATH Keywords

weightsspectrumirreducible unitary representationsintertwining operatorsinfinitesimal operatorsmost degenerate series

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Semisimple Lie groups and their representations (22E46)

Related Items (3)

The \((\mathfrak g,K)\)-module structures of principal series of \(\text{SU}(2,2)\) ⋮ Spectral decompositions of some representations of Lie groups ⋮ Degenerate principal series representations of \(GL_n(\mathbb{C})\) and \(GL_n(\mathbb{R})\)

Cites Work

• Intertwining operators for semisimple groups. II
• Intertwining operators for semisimple groups
• Representation matrix elements and Clebsch–Gordan coefficients of the semisimple Lie groups
• Matrix elements for infinitesimal operators of the groups U(p+q) and U(p,q) in a U(p) ×U(q) basis. I
• Representations of the groups GL(n,R) and SU(n) in an SO(n) basis
• Degenerate Representations of the Symplectic Groups II. The Noncompact Group Sp(p, q)

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