Racah operators for principal
Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 369-381 Cet article a éte moissonné depuis la source Math-Net.Ru

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As a generalization of the well-known Racah coefficients (which are usually defined for finite-dimensional representations of semisimple Lie groups), the concept of Racah operators is introduced for locally compact groups with a ‘nice’ dual space. Explicit expressions for these operators are presented for $\operatorname{PSL}(2,\mathbb C)$. Bibliography: 8 titles.
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R. S. Ismagilov. Racah operators for principal. Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 369-381. http://geodesic.mathdoc.fr/item/SM_2007_198_3_a2/

[1] P. I. Golod, A. U. Klimyk, Matematicheskie osnovy teorii simmetrii, RKhD, M., Izhevsk, 2001

[2] A. F. Nikiforov, S. K. Suslov, V. B. Uvarov, Klassicheskie ortogonalnye polinomy diskretnoi peremennoi, Nauka, M., 1985 ; A. F. Nikiforov, S. K. Suslov, V. B. Uvarov, Classical orthogonal polynomials of a discrete variable, Springer-Verlag, Berlin, 1991 | MR | Zbl | MR | Zbl

[3] V. A. Knyr, P. P. Pipiraite, Yu. F. Smirnov, “Kanonicheskie preobrazovaniya, “derevya” i momenty, kratnye 1/4”, Yadernaya fizika, 22:5 (1975), 1063–1072 | MR

[4] W. Groenevelt, “Wilson function transforms related to Racah coefficients”, Acta Appl. Math., 91:2 (2006), 133–191 ; arXiv: math.CA/0501511 | DOI | MR | Zbl

[5] M. A. Naimark, “Razlozhenie tenzornogo proizvedeniya neprivodimykh predstavlenii sobstvennoi gruppy Lorentsa na neprivodimye predstavleniya. I. Sluchai tenzornogo proizvedeniya predstavlenii osnovnoi serii”, Tr. MMO, 8 (1959), 121–154 | MR

[6] R. S. Ismagilov, “Ob operatorakh Raká ”, Funkts. analiz i ego pril., 40:3 (2006), 69–72 | MR | Zbl

[7] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Obobschennye funktsii. Vyp. 5. Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Fizmatgiz, M., 1962 ; I. M. Gel'fand, M. I. Graev, N. Ya. Vilenkin, Generalized functions. Vol. 5. Integral geometry and representation theory, Academic Press, New York–London, 1966 | MR | Zbl | MR | Zbl

[8] I. M. Gelfand, M. I. Graev, V. S. Retakh, “Gipergeometricheskie funktsii nad proizvolnym polem”, UMN, 59:5 (2004), 29–100 | MR | Zbl