Geodesic
Harmonic Analysis on a Class of Spherical Homogeneous Spaces
Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 703-711.

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

The spectrum of representations of a semisimple algebraic group in spaces of sections of homogeneous linear bundles on a certain class of spherical homogeneous spaces is studied; the algebra of invariant functions on the cotangent bundles of spaces from this class and invariant differential operators are described.
Keywords: semisimple complex algebraic group, irreducible representation, homogenous space, homogeneous linear bundle, spherical homogeneous space, cotangent bundle, invariant differential operator, Borel subgroup, universal enveloping algebra. 
@article{MZM_2011_90_5_a5,
     author = {N. E. Gorfinkel},
     title = {Harmonic {Analysis} on a {Class} of {Spherical} {Homogeneous} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {703--711},
     publisher = {mathdoc},
     volume = {90},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a5/}
}
TY  - JOUR
AU  - N. E. Gorfinkel
TI  - Harmonic Analysis on a Class of Spherical Homogeneous Spaces
JO  - Matematičeskie zametki
PY  - 2011
SP  - 703
EP  - 711
VL  - 90
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a5/
LA  - ru
ID  - MZM_2011_90_5_a5
ER  - 
%0 Journal Article
%A N. E. Gorfinkel
%T Harmonic Analysis on a Class of Spherical Homogeneous Spaces
%J Matematičeskie zametki
%D 2011
%P 703-711
%V 90
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a5/
%G ru
%F MZM_2011_90_5_a5
N. E. Gorfinkel. Harmonic Analysis on a Class of Spherical Homogeneous Spaces. Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 703-711. http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a5/

[1] N. E. Gorfinkel, “Spektr predstavlenii reduktivnoi gruppy $G$ v prostranstvakh sechenii odnorodnykh lineinykh rassloenii na $G/TU'$”, Letnyaya shkola-konferentsiya “Algebry Li, algebraicheskie gruppy i teoriya invariantov” (Samara, 8-15 iyunya 2009), Tezisy dokladov, Univers grupp, Samara, 2009, 15–16

[2] D. I. Panyushev, “Actions of the derived group of a maximal unipotent subgroup on $G$-varieties”, Int. Math. Res. Not., 2010, no. 4, 674–700 | MR | Zbl

[3] F. Knop, “Weylgruppe und Momentabbildung”, Invent. Math., 99:1 (1990), 1–23 | DOI | MR | Zbl

[4] F. Knop, “A Harish–Chandra homomorphism for reductive group actions”, Ann. of Math. (2), 140:2 (1994), 253–288 | DOI | MR | Zbl

[5] R. S. Avdeev, “Rasshirennye polugruppy starshikh vesov affinnykh sfericheskikh odnorodnykh prostranstv neprostykh poluprostykh algebraicheskikh grupp”, Izv. RAN. Ser. matem., 74:6 (2010), 3–26 | MR

[6] D. I. Panyushev, “Complexity and rank of homogeneous spaces”, Geom. Dedicata, 34:3 (1990), 249–269 | DOI | MR | Zbl

[7] D. A. Timashev, “Obobschenie razlozheniya Bryua”, Izv. RAN. Ser. matem., 58:5 (1994), 110–123 | MR | Zbl

[8] D. H. Collingwood, W. M. McGovern, Nilpotent Orbits in Semisimple Lie Algebras, Van Nostrand Reinhold Math. Ser., Van Nostrand Reinhold, New York, 1993 | MR | Zbl

[9] E. B. Vinberg, V. L. Popov, “Teoriya invariantov”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 55, VINITI, M., 1989, 137–309 | MR | Zbl

[10] B. Kostant, “The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group”, Amer. J. Math., 81 (1959), 973–1032 | DOI | MR | Zbl

[11] E. B. Vinberg, “Kommutativnye odnorodnye prostranstva i koizotropnye simplekticheskie deistviya”, UMN, 56:1 (2001), 3–62 | MR | Zbl