The matrix representations of g2. I. Representations in an so(4) basis

DOI10.1063/1.528025zbMath0654.17004OpenAlexW3042934473MaRDI QIDQ3800231

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Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528025

zbMATH Keywords

matrix representationmissing labelsVector Coherent Statebasis of vector holomorphic functionschain of subalgebrasexceptional Lie algebra \({\mathfrak g_ 2}\)explicit basis constructionsirreducible ladder representationsmissing internal labelsnilpotent raising operator algebrareal compact Lie algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Exceptional (super)algebras (17B25)

Related Items (7)

Vector-coherent-state theory as a theory of induced representations ⋮ Matrix representations of SOn+2 in an SOn×SO2 basis and some isoscalar factors for SOn+2⊇SOn×SO2 ⋮ Superfield and matrix realizations of highest weight representations for osp(m/2n) ⋮ The matrix representations of g2. II. Representations in an su(3) basis ⋮ The matrix representation of SO7 in an (SU2)3 basis ⋮ Highest weight representations for gl(m/n) and gl(m+n) ⋮ Vector coherent state theory of the generic representations of so(5) in an so(3) basis

Cites Work

• Coherent states of the real symplectic group in a complex analytic parametrization. I. Unitary-operator coherent states
• A pair of commuting scalars for G(2) ⊇ SU(2)×SU(2)
• Vector coherent state representation theory
• Vector coherent state theory and its application to the orthogonal groups
• New perspective on the U(n) Wigner-Racah calculus. II. Elementary reduced Wigner coefficients for U(n)
• Generating functions for G2 characters and subgroup branching rules
• Branching rules for classical Lie groups using tensor and spinor methods
• Quark structure and octonions
• On the irreducible representations of the Lie algebra chain G2⊇A2
• The evaluation of weight multiplicities of G₂
• Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras
• Properties of Overcomplete and Nonorthogonal Basis Vectors
• Internal-Labeling Problem
• Labeling States and Constructing Matrix Representations of G2

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