Structure and matrix elements of the degenerate series representations of U(p+q) and U(p,q) in a U(p)×U(q) basis

DOI10.1063/1.525530zbMath0548.22011OpenAlexW2015094880MaRDI QIDQ3341065

Bruno Gruber, A. U. Klimyk

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1063/1.525530

zbMATH Keywords

weightsspectrumintertwining operatorsirreducible representationscomposition seriesinfinitesimal operatorsmaximal parabolic subgroupmost 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 (8)

The \((\mathfrak g,K)\)-module structures of principal series of \(\text{SU}(2,2)\) ⋮ The matrix representation of U4 in the U2×U2 basis and some isoscalar factors for Up+q ⊇Up×Uq ⋮ Representations of the quantum algebras 𝒰q(u r,s) and 𝒰q(u r+s) related to the quantum hyperboloid and sphere ⋮ Spectral decompositions of some representations of Lie groups ⋮ Spectrum of the Dirac operator on complex projective space \(P_{2q- 1}({\mathbb{C}})\) ⋮ Infinitesimal operators and structure of the representations of the groups SO*(2n) and SO(2n) in a U(n) basis and of the groups SU*(2n) and SU(2n) in an Sp(n) basis ⋮ Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis ⋮ Infinitesimal operators of group representations in noncanonical bases

Cites Work

• Degenerate series representations of the universal covering group of SU(2,2)
• Unitary irreducible representations of SU(2,2)
• Degenerate representations of non-compact unitary groups. II: Continuous series
• 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
• Matrix elements for infinitesimal operators of the groups U(p+q) and U(p,q) in a U(p) ×U(q) basis. II

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