On biorthogonal and orthonormal Clebsch–Gordan coefficients of SU(3): Analytical and algebraic approaches

DOI10.1063/1.528119zbMath0663.22013OpenAlexW2145107053MaRDI QIDQ3812475

S. I. Ališauskas

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528119

zbMATH Keywords

biorthogonal systemscoupling coefficientscoupled statesdual isofactorsexternal missing label operatorsminimal coupled basesSU(3) outer multiplicity problem

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Semisimple Lie groups and their representations (22E46) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30)

Related Items (11)

Orthogonalization coefficients for the Elliott–Draayer states of the two parametric irreps of SU(n)⊇SO(n) ⋮ On the projected bases for Sp(4)⊇U(2) and the orthogonalization problem ⋮ Symmetry properties of matrix elements of canonical SU(3) tensor operators ⋮ Explicit orthonormal Clebsch–Gordan coefficients of SU(3) ⋮ Explicit canonical tensor operators and orthonormal coupling coefficients of SU(3) ⋮ Explicit orthogonalization of some biorthogonal bases for SU(n)⊇SO(n) and Sp(4)⊇U(2) ⋮ Complementary group resolution of the SU(n) outer multiplicity problem. I. The Littlewood rules and a complementary U(2n−2) group structure ⋮ Complementary group resolution of the SU(n) outer multiplicity problem. II. Recoupling approach for SU(3)⊃U(2) reduced Wigner coefficients ⋮ Towards the canonical tensor operators of u q(3). I. The maximal null space case ⋮ Towards the canonical tensor operators of uq(3). II. The denominator function problem ⋮ Comment on ‘‘The matrix representation of U4 in the U2×U2 basis and isoscalar factors for U p+q⊇U p×U q’’ [F. Pan, J. Math. Phys. 31, 1333 (1990)]

Cites Work

• Spectral resolution of \(\mathrm{SU}(3)\)-invariant solutions of the Yang-Baxter equation
• Representation matrix elements and Clebsch–Gordan coefficients of the semisimple Lie groups
• On the denominator function for canonical SU(3) tensor operators
• On the spectra of SO(3) scalars in the enveloping algebra of SU(3)
• Painless nonorthogonal expansions
• A resolution of the SU(3) outer multiplicity problem and computation of Wigner coefficients for SU(3)
• A solution to the SU(n) external state labelling problem based upon a U(n-1,n-1) group. I. General theory
• The polynomial-type analysis of SU(3) group-theoretical quantities
• Sum rules for the matrices of the generators of SU(3) in an SO(3) basis
• Internal-labeling operators
• Structural properties of the self-conjugate SU(3) tensor operators
• Wigner and Racah coefficients for SU3
• Algebraic Tabulation of Clebsch-Gordan Coefficients of SU3 for the Product (λ, μ)⊗ (1, 1) of Representations of SU3
• Bases for the Irreducible Representations of the Unitary Groups and Some Applications
• Recursion Relations for the Wigner Coefficients of Unitary Groups
• Representations of finite U3 transformations
• ON THE DEGENERACY PROBLEM IN SU(3)
• General Coupling Coefficients for the Group SU(3)
• Canonical Definition of Wigner Coefficients in Un
• Substitution Group and Mirror Reflection Symmetry in Special Unitary Groups
• On the Representations of the Semisimple Lie Groups. V. Some Explicit Wigner Operators for SU3
• Canonical Unit Adjoint Tensor Operators in U(n)
• On the Symmetric Tensor Operators of the Unitary Groups
• On the Evaluation of the Multiplicity-Free Wigner Coefficients of U(n)
• Nth rank tensor representations of U(n) symmetry adapted to subgroups of the symmetric group S N
• On the structure of the canonical tensor operators in the unitary groups. II. The tensor operators in U(3) characterized by maximal null space

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