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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya

Izv. RAN. Ser. Mat., 2023, Volume 87, Issue 6, Pages 3–34 (Mi im9150)

A functional realization of the Gelfand–Tsetlin base
D. V. Artamonov

References

1. I. M. Gelfand, M. L. Tsetlin, “Konechnomernye predstavleniya gruppy unimodulyarnykh matrits”, Dokl. AN SSSR, 71:5 (1950), 825–828  mathscinet  zmath
2. G. E. Baird, L. C. Biedenharn, “On the representations of semisimple Lie groups. II”, J. Math. Phys., 4:12 (1963), 1449–1466  crossref  mathscinet  zmath  adsnasa
3. D. V. Artamonov, “Clebsh–Gordan coefficients for the algebra $\mathfrak{gl}_3$ and hypergeometric functions”, St. Petersburg Math. J., 33:1 (2022), 1–22  mathnet  crossref  mathscinet  zmath
4. P. A. Valinevich, “Construction of the Gelfand–Tsetlin basis for unitary principal series representations of the algebra $\mathfrak{sl}_n(\mathbb C)$”, Theoret. and Math. Phys., 198:1 (2019), 145–155  mathnet  crossref  crossref  mathscinet  zmath  adsnasa
5. V. K. Dobrev, P. Truini, “Polynomial realization of $U_q(\mathrm{sl}(3))$ Gel'fand–(Weyl)–Zetlin basis”, J. Math. Phys., 38:7 (1997), 3750–3767  crossref  mathscinet  zmath  adsnasa
6. V. K. Dobrev, A. D. Mitov, P. Truini, “Normalized $U_q(\mathrm{sl}(3))$ Gel'fand–(Weyl)–Zetlin basis and new summation formulas for $q$-hypergeometric functions”, J. Math. Phys., 41:11 (2000), 7752–7768  crossref  mathscinet  zmath  adsnasa
7. D. V. Artamonov, “A Gelfand–Tsetlin-type basis for the algebra $\mathfrak{sp}_4$ and hypergeometric functions”, Theoret. and Math. Phys., 206:3 (2021), 243–257  mathnet  crossref  crossref  mathscinet  zmath  adsnasa
8. D. P. Želobenko, Compact Lie groups and their representations, Transl. Math. Monogr., 40, Amer. Math. Soc., Providence, RI, 1973, viii+448 pp.  crossref  mathscinet  mathscinet  zmath  zmath
9. I. M. Gelfand, M. I. Graev, V. S. Retah, “General hypergeometric systems of equations and series of hypergeometric type”, Russian Math. Surveys, 47:4 (1992), 1–88  mathnet  crossref  mathscinet  zmath
10. D. V. Artamonov, “Formula for the product of Gauss hypergeometric functions and applications”, J. Math. Sci. (N.Y.), 249 (2020), 817–826  crossref  mathscinet  zmath
11. I. M. Gelfand, A. V. Zelevinskii, M. M. Kapranov, “Hypergeometric functions and toral manifolds”, Funct. Anal. Appl., 23:2 (1989), 94–106  mathnet  crossref  mathscinet  zmath
12. J. Kamnitzer, “Geometric constructions of the irreducible representations of $GL_n$”, Geometric representation theory and extended affine Lie algebras (Ottawa, 2009), Fields Inst. Commun., 59, Amer. Math. Soc., Providence, RI, 2011, 1–18  mathscinet  zmath
13. V. Guillemin, S. Sternberg, “The Gelfand–Cetlin system and quantization of the complex flag manifolds”, J. Funct. Anal., 52:1 (1983), 106–128  crossref  mathscinet  zmath
14. T. M. Sadykov, A. K. Tsikh, Gipergeometricheskie i algebraicheskie funktsii mnogikh peremennykh, Nauka, M., 2014, 408 pp.
15. E. Miller, B. Sturmfels, Combinatorial commutative algebra, Grad. Texts in Math., 227, Springer-Verlag, New York, 2005, xiv+417 pp.  crossref  mathscinet  zmath
16. R. L. Graham, D. E. Knuth, O. Patashnik, Concrete mathematics. A foundation for computer science, 2nd ed., Addison-Wesley Publ. Co., Reading, MA, 1994, xiv+657 pp.  mathscinet  zmath


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