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.
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.
@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 = {http://www.numdam.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 DA - 1995/// SP - 929 EP - 950 VL - 45 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1479/ UR - https://zbmath.org/?q=an%3A0831.14022 UR - https://www.ams.org/mathscinet-getitem?mr=96i:14039 UR - https://doi.org/10.5802/aif.1479 DO - 10.5802/aif.1479 LA - en ID - AIF_1995__45_4_929_0 ER -
Panyushev, Dmitri I. Reductive group actions on affine varieties and their doubling. Annales de l'Institut Fourier, Tome 45 (1995) no. 4, pp. 929-950. doi : 10.5802/aif.1479. http://www.numdam.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 85a:14031 | Zbl 0475.14038
,[B2] Groupe de Picard et nombres caractéristiques des variétés sphériques, Duke Math. J., 58 (1989), 397-424. | MR 90i:14048 | Zbl 0701.14052
,[HH] Projective invariants of four subspaces, Preprint. | Zbl 0852.15021
, ,[KR] Orbits and representations associated with symmetric spaces, Amer. J. Math., 93 (1971), 753-809. | MR 47 #399 | Zbl 0224.22013
, ,[Li] On spherical double cones, J. Algebra, 166 (1994), 142-157. | MR 95c:14066 | Zbl 0823.20040
,[Lu] Adhérences d'orbite et invariants, Invent. Math., 29 (1975), 231-238. | MR 51 #12879 | Zbl 0315.14018
,[LR] A generalization of the Chevalley restriction theorem, Duke Math. J., 46 (1979), 487-496. | MR 80k:14049 | Zbl 0444.14010
, ,[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 88h:14047 | Zbl 0663.20044
,[P2] Complexity and rank of homogeneous spaces, Geom. Dedicata, 34 (1990), 249-269. | MR 92e:14046 | Zbl 0706.14032
,[P3] Complexity and rank of double cones and tensor product decompositions, Comment. Math. Helv., 68 (1993), 455-468. | MR 94g:14025 | Zbl 0804.14024
,[P4] Complexity and nilpotent orbits, Manuscripta Math., 83 (1994), 223-237. | MR 95e:14039 | Zbl 0822.14024
,[P5] A restriction theorem and the Poincaré series for U-invariants, Math. Annalen, 301 (1995), 655-675. | MR 96d:13005 | Zbl 0820.14033
,[P6] Good properties of algebras of invariants and defect of linear representations, J. Lie Theory, 5 (1995). | MR 96j:14034 | Zbl 0845.14008
,[Po1] A stability criterion for an action of a semisimple group on a factorial variety, Math. USSR-Izv., 4 (1971), 527-535. | Zbl 0261.14011
,[Po2] Contractions of the actions of reductive algebraic groups, Math. USSR-Sbornik, 58 (1987), 311-335. | Zbl 0627.14033
,[Ri] On orbits of algebraic groups and Lie groups, Bull. Austral. Math. Soc., 25 (1982), 1-28. | MR 83i:14041 | Zbl 0467.14008
,[Sch1] Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978), 1-12. | MR 80c:14008 | Zbl 0391.20033
,[Sch2] Lifting smooth homotopies of orbit spaces, Publ. Math. I.H.E.S., 51 (1980), 37-135. | Numdam | MR 81h:57024 | Zbl 0449.57009
,[VP1] On a class of quasihomogeneous affine varieties, Math. USSR-Izv., 6 (1972), 743-758. | MR 47 #1815 | Zbl 0255.14016
, ,[VP2] Invariant theory, in : “Encyclopaedia Math. Sci.” 55, Berlin, Springer, 1994, 123-284. | Zbl 0789.14008
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