On an infinitesimal approach to semisimple Lie groups and raising and lowering operators of O(n) and U(n)

DOI10.1063/1.524441zbMath0445.22010OpenAlexW2073407808WikidataQ60732505 ScholiaQ60732505MaRDI QIDQ3889299

Mark D. Gould

Publication date: 1980

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

Full work available at URL: https://espace.library.uq.edu.au/view/UQ:299692/UQ299692_OA.pdf

zbMATH Keywords

reduced matrix elementsWigner coefficientsraising and lowering operators

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46) General properties and structure of real Lie groups (22E15)

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Cites Work

• On the tensor product of a finite and an infinite dimensional representation
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• Algebraic identities among U (n) infinitesimal generators
• Eigenvalues of the Casimir operators of the orthogonal and symplectic groups
• Casimir invariants and vector operators in simple and classical Lie algebras
• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• On the Representations of the Semisimple Lie Groups. II
• Invariant Operators of the Unitary Unimodular Group in n Dimensions
• Representations of the Orthogonal Group. I. Lowering and Raising Operators of the Orthogonal Group and Matrix Elements of the Generators
• Canonical Definition of Wigner Coefficients in Un
• Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs
• Canonical Unit Adjoint Tensor Operators in U(n)
• Characteristic Identities for Generators of GL(n), O(n) and Sp(n)
• Relativistic wave equations