Reduction of spherical functions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 54-68 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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
@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
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/

[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