Optimally defined Racah–Casimir operators for su(n) and their eigenvalues for various classes of representations

DOI10.1063/1.1322076zbMath1032.17009arXivmath-ph/0006013OpenAlexW2044279584MaRDI QIDQ2774668

Alan J. Macfarlane, José A. de Azcárraga

Publication date: 26 February 2002

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

Full work available at URL: https://arxiv.org/abs/math-ph/0006013

zbMATH Keywords

canonical pathOmega tensorsRacah-Casimir operatorsgeneralized Dynkin indexLie algebra cohomology cocycleprimitive Casimir operatorssimple compact Lie algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (6)

A quantummechanical derivation of the eigenvalues of the quadratic Casimir operator of the algebra \(SU (n)\) in Young tableau representation ⋮ Two-dimensional superintegrable systems from operator algebras in one dimension ⋮ Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials ⋮ COMPILATION OF RELATIONS FOR THE ANTISYMMETRIC TENSORS DEFINED BY THE LIE ALGEBRA COCYCLES OF su(n) ⋮ LIE ALGEBRA AND INVARIANT TENSOR TECHNOLOGY FOR g₂ ⋮ Hidden supersymmetries in supersymmetric quantum mechanics

Cites Work

• Higher-order simple Lie algebras
• Invariant tensors for simple groups
• COMPILATION OF RELATIONS FOR THE ANTISYMMETRIC TENSORS DEFINED BY THE LIE ALGEBRA COCYCLES OF su(n)
• On characteristic equations, trace identities and Casimir operators of simple Lie algebras
• Modified fourth-order Casimir invariants and indices for simple Lie algebras
• Semisimple subalgebras of semisimple Lie algebras
• General indices of representations and Casimir invariants
• Higher indices of group representations
• Casimir invariants and vector operators in simple and classical Lie algebras
• GROUP THEORY FACTORS FOR FEYNMAN DIAGRAMS
• An explicit construction of Casimir operators and eigenvalues. II
• Algebraic Tabulation of Clebsch-Gordan Coefficients of SU3 for the Product (λ, μ)⊗ (1, 1) of Representations of SU3
• Fermionic realisations of simple Lie algebras and their invariant fermionic operators

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