Clebsh–Gordan coefficients for the algebra 𝔤𝔩₃ and hypergeometric functions

DOI10.1090/spmj/1686OpenAlexW4213280943MaRDI QIDQ5020275

Dmitry V. Artamonov

Publication date: 5 January 2022

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.01049

zbMATH Keywords

Clebsch-Gordan coefficients\(A\)-hypergeometric functionsGelfand-Tsetlin base

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (6)

The Gelfand–Tsetlin basis for infinite-dimensional representations of gln(C) ⋮ Formulas for calculating the \(3j\)-symbols of the representations of the Lie algebra \({\mathfrak{gl}}_3\) for the Gelfand-Tsetlin bases ⋮ Classical \(6j\)-symbols of finite-dimensional representations of the algebra \(\mathfrak{gl}_3\) ⋮ A functional realization of the Gelfand-Tsetlin base ⋮ A functional approach to a Gelfand-Tsetlin type base for $\mathfrak{o}_5$ ⋮ A Gelfand-Tsetlin-type basis for the algebra \(\mathfrak{sp}_4\) and hypergeometric functions

Cites Work

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• On a resolution of the multiplicity problem for U(n)
• \(SU\)(3) Clebsch-Gordan coefficients with definite permutation symmetry
• A pattern calculus for tensor operators in the unitary groups
• Some special SU(3)⊇R(3) Wigner coefficients and their application
• Explicit canonical tensor operators and orthonormal coupling coefficients of SU(3)
• General hypergeometric systems of equations and series of hypergeometric type
• An algebraic algorithm for calculating Clebsch–Gordan coefficients; application to SU(2) and SU(3)
• A numerical algorithm for the explicit calculation of SU(N) and $\mbox{SL}(N,\mathbb {C})$SL(N,C) Clebsch–Gordan coefficients
• A calculus for SU(3) leading to an algebraic formula for the Clebsch–Gordan coefficients
• On the Representations of the Semisimple Lie Groups. II
• Wigner Coefficients for the S<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">U</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Group and some Applications
• 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 Evaluation of the Multiplicity-Free Wigner Coefficients of U(n)
• On the structure of the canonical tensor operators in the unitary groups. I. An extension of the pattern calculus rules and the canonical splitting in U(3)

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