Formulas for calculating the \(3j\)-symbols of the representations of the Lie algebra \({\mathfrak{gl}}_3\) for the Gelfand-Tsetlin bases

DOI10.1134/S0037446622040012zbMath1503.17015WikidataQ113785964 ScholiaQ113785964MaRDI QIDQ2160174

Dmitry V. Artamonov

Publication date: 3 August 2022

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

hypergeometric functionClebsch-Gordan coefficient\( 3j \)-symbol

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (1)

Classical \(6j\)-symbols of finite-dimensional representations of the algebra \(\mathfrak{gl}_3\)

Cites Work

• Semigroups of \(sl_3(\mathbb C)\) tensor product invariants
• On the matrices of Clebsch-Gordan coefficients
• Formula for the product of Gauss hypergeometric functions and applications
• A pattern calculus for tensor operators in the unitary groups
• The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
• General hypergeometric systems of equations and series of hypergeometric type
• Clebsh–Gordan coefficients for the algebra 𝔤𝔩₃ and hypergeometric functions
• On the Representations of the Semisimple Lie Groups. II
• 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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