Formulas for Calculating the -Symbols of the Representations of the Lie Algebra  for the Gelfand–Tsetlin Bases

We give a simple explicit formula for an arbitrary -symbol for the Lie algebra  . The symbol is expressed as the ratio of values of hypergeometric functions with substituted for all arguments. Finding a  -symbol is essentially equivalent to the determination of an arbitrary Clebsch–Gordan coefficien...

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Bibliographic Details
Published in:Siberian mathematical journal 2022, Vol.63 (4), p.595-610
Main Author: Artamonov, D. V.
Format: Article
Language:English
Subjects:
Hypergeometric functions
Lie groups
Mathematical analysis
Mathematics
Mathematics and Statistics
Quantum mechanics
Online Access:Get full text
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Summary:We give a simple explicit formula for an arbitrary -symbol for the Lie algebra  . The symbol is expressed as the ratio of values of hypergeometric functions with substituted for all arguments. Finding a  -symbol is essentially equivalent to the determination of an arbitrary Clebsch–Gordan coefficient for  . The coefficients are important in the quark theory of quantum mechanics.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622040012