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JOURNALS // Sibirskii Matematicheskii Zhurnal

Sibirsk. Mat. Zh., 2022, Volume 63, Number 4, Pages 717–735 (Mi smj7688)

Formulas for calculating the $3j$-symbols of the representations of the Lie algebra $\mathfrak{gl}_3$ for the Gelfand–Tsetlin bases
D. V. Artamonov

References

1. Bidenkharn L., Lauk Dzh., Uglovoi moment v kvantovoi fizike, Mir, M., 1984
2. Greiner W., Muller B., Quantum mechanics. Symmetries, 2nd ed., Springer-Verl., Berlin, 1994  mathscinet  zmath
3. van der Waerden B. L., Die gruppentheoretische Methode in der Quantenmechanik, Julius Springer-Verl., Berlin, 1932  mathscinet  zmath
4. Godunov S. K., Mikhailova T. Yu., Predstavleniya gruppy vraschenii i sfericheskie funktsii, Nauch. kniga, Novosibirsk, 1998  mathscinet
5. Godunov S. K., Gordienko V. M., “Koeffitsienty Klebsha — Gordana pri razlichnykh vyborakh bazisov unitarnykh i ortogonalnykh predstavlenii grupp $SU(2)$, $SO(3)$”, Sib. mat. zhurn., 45:3 (2004), 540–557  mathnet  mathscinet  zmath
6. Gordienko V. M., “Matritsy iz koeffitsientov Klebsha — Gordana”, Sib. mat. zhurn., 58:6 (2017), 1276–1291  mathnet  mathscinet  zmath
7. Selivanova S. V., “Invariantnaya zapis uravnenii teorii uprugosti”, Zhurn. prikl. matematiki i tekhn. fiziki, 49:5 (2008), 127–142  mathscinet
8. Baid G. E., Biedenharn L. C., “On the representations of semisimple Lie groups II”, J. Math. Phys., 4:12 (1963), 1449–1466  crossref  mathscinet  adsnasa
9. Biedenharn L. C., Louck J. D., “A pattern calculus for tensor operators in the unitary groups”, Comm. Math. Phys., 8:2 (1968), 89–131  crossref  mathscinet  adsnasa
10. Biedenharn L. C., Louck J. D., “A pattern calculus for tensor operators in the unitary groups”, Comm. Math. Phys., 8:2 (1968), 89–131  crossref  mathscinet  adsnasa
11. Biedenharn L. C., Louck J. D., “Canonical adjoint tensor operators in $U(n)$”, J. Math. Phys., 11:8 (1970), 2368–2411  crossref  mathscinet  adsnasa
12. Biedenharn L. C., Ciftan M., Chacón E., “On the evaluation of the multiplicity-free Wigner coefficients of $U(n)$”, J. Math. Phys., 13:5 (1972), 577–589  crossref  mathscinet  adsnasa
13. Biedenharn L. C., Louck J. D., “On the structure of the canonical tensor operators in the unitary groups. II. An extension of the pattern calculus rules and the canonical splitting in $U(3)$”, J. Math. Phys., 13:12 (1972), 1957–1984  crossref  mathscinet  zmath  adsnasa
14. Artamonov D. V., “Koeffitsienty Klebsha — Gordana dlya $\mathfrak{gl}_3$ i gipergeometricheskie funktsii”, Algebra i analiz, 33:1 (2021), 1–29  mathnet  mathscinet
15. Artamonov D. V., “Formula for the product of Gauss hypergeometric functions and applications”, J. Math. Sci., 249 (2020), 1–29  crossref  mathscinet
16. Zhelobenko D. P., Kompaktnye gruppy Li i ikh predstavleniya, MTsNMO, M., 2007
17. Gelfand I. M., Graev M. I., Retakh V. S., “Obschie gipergeometricheskie sistemy uravnenii i ryady gipergeometricheskogo tipa”, Uspekhi mat. nauk, 47:4 (1992), 3–82  mathnet  mathscinet  zmath
18. Klyachko A. A., Stable vector bundles and Hermitian operators, Preprint, University of Marne-la-Vallee, 1994  mathscinet
19. Knutson A., Tao T., “The honeycomb model of $GL_n({\Bbb C})$ tensor products I: Proof of the saturation conjecture”, J. Amer. Math. Soc., 12:4 (1999), 1055–1090  crossref  mathscinet  zmath
20. Manon C., Zhou Z., “Semigroups of $sl_2({\Bbb C})$ tensor product invariants”, J. Algebra, 400 (2014), 94–104  crossref  mathscinet  zmath


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