Geodesic
On Spherical Functions on the Group $\operatorname{SU}\times\operatorname{SU}\times\operatorname{SU}$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 1, pp. 59-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the group $G:=\operatorname{SU}\times\dots\times\operatorname{SU}$ ($l$ factors), where $\operatorname{SU}(2)$ is the group of unitary $2\times 2$ matrices with unit determinant. Let $K\simeq\operatorname{SU}(2)$ be the diagonal subgroup of $G$. We obtain the generating function of all $K$-spherical functions on $G$.
Keywords: spherical function, Fock space, invariant of $\operatorname{SU}(2)$.
Mots-clés : orthogonal polynomial 
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Yu. A. Neretin. On Spherical Functions on the Group $\operatorname{SU}\times\operatorname{SU}\times\operatorname{SU}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 1, pp. 59-67. http://geodesic.mathdoc.fr/item/FAA_2010_44_1_a4/

[1] D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl

[2] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 | MR | Zbl

[3] N. Ya. Vilenkin, A. U. Klimyk, Representations of Lie Groups and Special Functions, 1, Kluwer, 1992 | MR

[4] M. Krämer, “Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen”, Composito Math., 38:2 (1979), 129–153 | MR | Zbl

[5] F. Knop, B. Van Steirteghem, “Classification of smooth affine spherical varieties”, Transform. Groups, 11:3 (2006), 495–516 | DOI | MR | Zbl

[6] R. Howe, “Transcending classical invariant theory”, J. Amer. Math. Soc., 2:3 (1989), 535–552 | DOI | MR | Zbl

[7] A. A. Klyachko, “Spatial polygons and stable configurations of points on a projective line”, Algebraic geometry and applications (Yaroslavl, 1992), Vieweg, Braunschweig, 1994, 67–84 | DOI | MR | Zbl

[8] A. Varchenko, Special functions, KZ type equations and representation theory, Amer. Math. Soc., Providence, RI, 2003 | MR | Zbl

[9] H. Rosengren, “An elementary approach to $6j$-symbols (classical, quantum, rational trigonometric, and elliptic)”, Ramanujan J., 13:1-3 (2007), 131–166 | DOI | MR | Zbl

[10] Kategorii simmetrii i beskonechnomernye gruppy, Editorial URSS, M., 1998