We study -actions of the form , where is the dual (to ) -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action is given. It is shown that the doubled actions have a number of nice properties, if is spherical or of complexity one.
Nous étudions les actions de la forme où est la -variété duale de . Ces actions sont appelées les doubles. Nous donnons une interprétation géométrique de la complexité de l’action . Nous montrons que les actions doublées ont un certain nombre de bonnes propriétés, lorsque est sphérique ou de complexité un.
@article{AIF_1995__45_4_929_0, author = {Panyushev, Dmitri I.}, title = {Reductive group actions on affine varieties and their doubling}, journal = {Annales de l'Institut Fourier}, pages = {929--950}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {4}, year = {1995}, doi = {10.5802/aif.1479}, zbl = {0831.14022}, mrnumber = {96i:14039}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1479/} }
TY - JOUR AU - Panyushev, Dmitri I. TI - Reductive group actions on affine varieties and their doubling JO - Annales de l'Institut Fourier PY - 1995 SP - 929 EP - 950 VL - 45 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1479/ DO - 10.5802/aif.1479 LA - en ID - AIF_1995__45_4_929_0 ER -
%0 Journal Article %A Panyushev, Dmitri I. %T Reductive group actions on affine varieties and their doubling %J Annales de l'Institut Fourier %D 1995 %P 929-950 %V 45 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1479/ %R 10.5802/aif.1479 %G en %F AIF_1995__45_4_929_0
Panyushev, Dmitri I. Reductive group actions on affine varieties and their doubling. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 929-950. doi : 10.5802/aif.1479. https://aif.centre-mersenne.org/articles/10.5802/aif.1479/
[B1] Invariants d'un sous-groupe unipotent maximal d'un groupe semi-simple, Ann. Inst. Fourier, 33-1 (1983), 1-27. | Numdam | MR | Zbl
,[B2] Groupe de Picard et nombres caractéristiques des variétés sphériques, Duke Math. J., 58 (1989), 397-424. | MR | Zbl
,[HH] Projective invariants of four subspaces, Preprint. | Zbl
, ,[KR] Orbits and representations associated with symmetric spaces, Amer. J. Math., 93 (1971), 753-809. | MR | Zbl
, ,[Li] On spherical double cones, J. Algebra, 166 (1994), 142-157. | MR | Zbl
,[Lu] Adhérences d'orbite et invariants, Invent. Math., 29 (1975), 231-238. | MR | Zbl
,[LR] A generalization of the Chevalley restriction theorem, Duke Math. J., 46 (1979), 487-496. | MR | Zbl
, ,[P1] Orbits of maximal dimension of solvable subgroups of reductive algebraic groups and reduction for U-invariants, Math. USSR-Sb., 60 (1988), 365-375. | MR | Zbl
,[P2] Complexity and rank of homogeneous spaces, Geom. Dedicata, 34 (1990), 249-269. | MR | Zbl
,[P3] Complexity and rank of double cones and tensor product decompositions, Comment. Math. Helv., 68 (1993), 455-468. | MR | Zbl
,[P4] Complexity and nilpotent orbits, Manuscripta Math., 83 (1994), 223-237. | MR | Zbl
,[P5] A restriction theorem and the Poincaré series for U-invariants, Math. Annalen, 301 (1995), 655-675. | MR | Zbl
,[P6] Good properties of algebras of invariants and defect of linear representations, J. Lie Theory, 5 (1995). | MR | Zbl
,[Po1] A stability criterion for an action of a semisimple group on a factorial variety, Math. USSR-Izv., 4 (1971), 527-535. | Zbl
,[Po2] Contractions of the actions of reductive algebraic groups, Math. USSR-Sbornik, 58 (1987), 311-335. | Zbl
,[Ri] On orbits of algebraic groups and Lie groups, Bull. Austral. Math. Soc., 25 (1982), 1-28. | MR | Zbl
,[Sch1] Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978), 1-12. | MR | Zbl
,[Sch2] Lifting smooth homotopies of orbit spaces, Publ. Math. I.H.E.S., 51 (1980), 37-135. | Numdam | MR | Zbl
,[VP1] On a class of quasihomogeneous affine varieties, Math. USSR-Izv., 6 (1972), 743-758. | MR | Zbl
, ,[VP2] Invariant theory, in : “Encyclopaedia Math. Sci.” 55, Berlin, Springer, 1994, 123-284. | Zbl
, ,Cited by Sources: