Reduction of spherical functions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 54-68

Voir la notice de l'article provenant de la source Math-Net.Ru

Using reduction of spherical functions we obtain generators of the algebra and fields of invariants for the coadjoint representation of Borel and maximal unipotent subalgebras of simple Lie algebras.
Keywords: spherical function, algebra of invariants.
Mots-clés : coadjoint representation
A. N. Panov. Reduction of spherical functions. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 54-68. http://geodesic.mathdoc.fr/item/VSGU_2010_6_a6/
@article{VSGU_2010_6_a6,
     author = {A. N. Panov},
     title = {Reduction of spherical functions},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {54--68},
     year = {2010},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2010_6_a6/}
}
TY  - JOUR
AU  - A. N. Panov
TI  - Reduction of spherical functions
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2010
SP  - 54
EP  - 68
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VSGU_2010_6_a6/
LA  - ru
ID  - VSGU_2010_6_a6
ER  - 
%0 Journal Article
%A A. N. Panov
%T Reduction of spherical functions
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2010
%P 54-68
%N 6
%U http://geodesic.mathdoc.fr/item/VSGU_2010_6_a6/
%G ru
%F VSGU_2010_6_a6

[1] Miyata K., “Invariants of certain groups”, Nagoya Math. J., 41 (1971), 69–73 | MR | Zbl

[2] Vinberg E. B., “Ratsionalnost polya invariantov treugolnoi gruppy”, Vestnik MGU. Ser. Matematicheskaya, 1982, no. 2, 23–24 | MR | Zbl

[3] Kirillov A. A., “Unitarnye predstavleniya nilpotentnykh grupp Li”, UMN, 17 (1962), 57–110 | MR | Zbl

[4] Kirillov A. A., Lektsii po metodu orbit, Nauchnaya kniga, Novosibirsk, 2002

[5] P. Deift et al., “The Toda flow on a generic orbit is integrable”, Comm. Pure Appl. Math., 39:2 (1986), 183–232 | DOI | MR | Zbl

[6] Arkhangelskii A. A., “Ob integrirovanii uravneniya Eilera na algebre treugolnykh matrits”, Matem. sbornik, 108:1 (1979), 134–142 | MR

[7] Perelomov A. M., Integriruemye sistemy klassicheskoi mekhaniki i algebry Li, Nauka, M., 1990, 240 pp. | Zbl

[8] Joseph A. A., “Preparation theorem for the prime spectrum of a semisimple Lie algebra”, J. Algebra, 48 (1977), 241–289 | DOI | MR | Zbl

[9] Joseph A., “The enigma of the missing invariants on the nilradical of a Borel”, Bull. Sci. math., 128 (2004), 433–446 | DOI | MR | Zbl

[10] Fauquant-Millet F., Joseph A., “Semi-centre de l'algébre enveloppante d'une sous-algebre parabolique d'une algébre de Lie semi-simple”, Ann. Scient. Ec. Norm. Sup. 4 serie, 38 (2005), 155–191 | MR | Zbl

[11] Trofimov V. V., “Uravnenie Eilera na borelevskikh podalgebrakh poluprostykh algebr Li”, Izv. AN SSSR. Ser. Matematicheskaya, 43:3 (1979), 715–733 | MR | Zbl

[12] Trofimov V. V., “Konechnomernye predstavleniya algebr Li i integriruemye sistemy”, Matem. sbornik, 111(153):4 (1980), 610–621 | MR | Zbl

[13] Trofimov V. V., “Semi-invariants of a Co-adjoint Representation of Borel Subalgebras of Simple Lie Algebras”, Selecta Math. Sovietica, 8:1 (1989), 31–56 | Zbl

[14] Gekhtman M. I., Shapiro M. Z., “Noncommutative and Commutative Integrability of Generic Toda Flows in Simple Lie algebras”, Comm. Pure Appl. Math., 52 (1999), 53–84 | 3.0.CO;2-5 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[15] Diksme Zh., Universalnye obertyvayuschie algebry, Mir, M., 1978, 408 pp. | MR

[16] Burbaki N., Gruppy i algebry Li, glavy IV-VI, Mir, M., 1972, 331 pp. | MR

[17] Serr Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969, 375 pp. | MR | Zbl