Geodesic
A Classification of Reductive Linear Groups with Spherical Orbits
Ivan Arzhantsev1, 2, 3, 4, 5
1Chair of Algebra, Moscow State University, Vorobievy Gory, Moscow 119899, Russia
2We classify finite dimensional G-modules V of an algebraic reductive group G such that any G-orbit in V is spherical. It is shown that any module with this property can be realized as a spherical module after an extension of the group by a central torus.
3Keywords: Reductive groups, spherical modules, algebras of invariants.
4MSC: 20G05, 17B10; 14M17, 14R20
5[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 289-299

Voir la notice de l'article provenant de la source Heldermann Verlag

We classify finite dimensional G-modules V of an algebraic reductive group G such that any G-orbit in V is spherical. It is shown that any module with this property can be realized as a spherical module after an extension of the group by a central torus.
Classification : 20G05, 17B10, 14M17, 14R20
Mots-clés : Reductive groups, spherical modules, algebras of invariants

Ivan Arzhantsev  1 , 2 , 3 , 4 , 5

1 Chair of Algebra, Moscow State University, Vorobievy Gory, Moscow 119899, Russia
2 We classify finite dimensional G-modules V of an algebraic reductive group G such that any G-orbit in V is spherical. It is shown that any module with this property can be realized as a spherical module after an extension of the group by a central torus.
3 Keywords: Reductive groups, spherical modules, algebras of invariants.
4 MSC: 20G05, 17B10; 14M17, 14R20
5 [ 
Ivan Arzhantsev. A Classification of Reductive Linear Groups with Spherical Orbits. Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 289-299. http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a14/
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     title = {A {Classification} of {Reductive} {Linear} {Groups} with {Spherical} {Orbits}},
     journal = {Journal of Lie Theory},
     pages = {289--299},
     year = {2002},
     volume = {12},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a14/}
}
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