Linear models for reductive group actions on affine quadrics
Doebeli, Michael
Bulletin de la Société Mathématique de France, Tome 122 (1994), p. 505-531 / Harvested from Numdam
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@article{BSMF_1994__122_4_505_0,
     author = {Doebeli, Michael},
     title = {Linear models for reductive group actions on affine quadrics},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {122},
     year = {1994},
     pages = {505-531},
     doi = {10.24033/bsmf.2244},
     mrnumber = {95j:14066},
     zbl = {0819.14018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BSMF_1994__122_4_505_0}
}

Doebeli, Michael. Linear models for reductive group actions on affine quadrics. Bulletin de la Société Mathématique de France, Tome 122 (1994) pp. 505-531. doi : 10.24033/bsmf.2244. http://gdmltest.u-ga.fr/item/BSMF_1994__122_4_505_0/

[1] Asoh (T.). - Compact transformation groups on ℤ2-cohomology spheres with orbit of codimension 1, Hiroshima Math. J., t. 11, 1981, p. 571-616. | MR 83b:57021 | Zbl 0515.57021

[2] Borel (A.). - Some remarks about Lie groups transitive on spheres and tori, Bull. Amer. Math. Soc., t. 55, 1949, p. 580-586. | MR 10,680c | Zbl 0034.01603

[3] Borel (A.). - Le plan projectif des octaves et les sphères comme espaces homogènes, C.R. Acad. Sci. Paris, t. 250, 1950, p. 1378-1381. | MR 11,640c | Zbl 0041.52203

[4] Borel (A.). - Les bouts des espaces homogènes de groupes de Lie, Ann. of Math., t. 58, 1953, p. 443-457. | MR 15,199c | Zbl 0053.13002

[5] Borel (A.). - Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math., t. 57, 1953, p. 115-207. | MR 14,490e | Zbl 0052.40001

[6] Borel (A.). - Seminar on Transformation Groups. - Princeton University Press, Princeton, New Jersey, 1960. | MR 22 #7129 | Zbl 0091.37202

[7] Bredon (G.E.). - On homogenous cohomology spheres, Ann. of Math., t. 73, 1961, p. 556-565. | MR 23 #A243 | Zbl 0102.38701

[8] Dadok (J.). - Orthogonal polar representations, Trans. Am. Math. Soc., t. 288, 1985, p. 125-137. | MR 86k:22019

[9] Dadok (J.) and Kac (V.). - Polar representations, J. Algebra, t. 92, 1985, p. 504-524. | MR 86e:14023 | Zbl 0611.22009

[10] Gizatullin (M.H.) and Danilov (V.I.). - Automorphisms of affine surfaces II, Math. USSR Isv., t. 11, 1977, p. 51-98. | MR 55 #10469 | Zbl 0379.14002

[11] Kambayashi (T.). - Automorphism group of a polynomial ring and algebraic group action on affine space, J. Algebra, t. 60, 1979, p. 439-451. | MR 81e:14026 | Zbl 0429.14017

[12] Knop (F.). - Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Räumen, Invent. math., t. 105, 1991, p. 217-220. | MR 92c:14046 | Zbl 0739.20019

[13] Kraft (H.). - Geometrische Methoden in der Invariantentheorie, Aspekte der Mathematik D1, Vieweg, Braunschweig/Wiesbaden, 1984. | MR 86j:14006 | Zbl 0669.14003 | Zbl 0569.14003

[14] Kraft (H.). - Algebraic automorphisms of affine space, Topological methods in algebraic transformation groups, (eds. H. Kraft, T. Petrie, G. W. Schwarz), Progress in Mathematics, vol. 80, Birkhäuser Verlag, Basel-Boston, 1989, p. 81-105. | MR 91g:14044 | Zbl 0719.14030

[15] Kraft (H.), Petrie (T.) and Randall (J.D.). - Quotient Varieties, Adv. Math., t. 74, 1989, p. 145-162. | MR 90b:14057 | Zbl 0691.14029

[16] Kraft (H.) and Schwartz (G.W.). - Reductive group actions with 1-dimensional quotient, Inst. Hautes Études Sci. Publ. Math., t. 76, 1992, p. 1-97. | Numdam | MR 94e:14065 | Zbl 0783.14026

[17] Littelmann (P.). - Koreguläre und äquidimensionale Darstellungen, J. Algebra, t. 123, 1989, p. 193-222. | MR 90e:20039 | Zbl 0688.14042

[18] Luna (D.). - Slices étales, Bull. Soc. Math. France, t. 33, 1973, p. 81-105. | Numdam | MR 49 #7269 | Zbl 0286.14014

[19] Montgomery (D.) and Samelson (H.). - Transformation groups of spheres, Ann. of Math., t. 44, 1943, p. 454-470. | MR 5,60b | Zbl 0063.04077

[20] Mostow (G.D.). - On covariant fiberings of Klein spaces II, Amer. J. Math., t. 84, 1962, p. 466-474. | MR 26 #257 | Zbl 0123.16303

[21] Poncet (J.). - Groupes de Lie compacts de transformations de l'espace euclidien et les sphères comme espaces homogènes, Comm. Math. Helv., t. 33, 1959, p. 109-120. | MR 21 #2708 | Zbl 0084.19006

[22] Schwartz (G.W.). - Lifting smooth homotopies of orbit spaces, Inst. Hautes Études Sci. Publ. Math., t. 51, 1978, p. 37-135. | Numdam | Zbl 0449.57009

[23] Schwartz (G.W.). - Exotic algebraic group actions, C. R. Acad. Sci. Paris, t. 309, 1989, p. 89-94. | MR 91b:14066 | Zbl 0688.14040

[24] Slodowy (P.). - Der Scheibensatz für algebraische Transformations-gruppen, Algebraic Transformation Groups and Invariant Theory, DMV Seminar vol. 13, Birkhäuser Verlag, Basel-Boston, 1989, p. 89-113. | MR 1044587 | Zbl 0682.00008 | Zbl 0722.14031

[25] Wang (H.C.). - Compact transformation groups of Sn with an (n − 1)-dimensional orbit, Amer. J. Math., t. 82, 1960, p. 698-748. | Zbl 0134.19404