@article{ASENS_1995_4_28_3_253_0, author = {Schwarz, Gerald W.}, title = {Lifting differential operators from orbit spaces}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {28}, year = {1995}, pages = {253-305}, doi = {10.24033/asens.1714}, mrnumber = {96f:14061}, zbl = {0836.14032}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_1995_4_28_3_253_0} }
Schwarz, Gerald W. Lifting differential operators from orbit spaces. Annales scientifiques de l'École Normale Supérieure, Tome 28 (1995) pp. 253-305. doi : 10.24033/asens.1714. http://gdmltest.u-ga.fr/item/ASENS_1995_4_28_3_253_0/
[AP] Stationary subgroups of points of general position in the representation space of a semisimple Lie group (Functional Anal. Appl., Vol. 5, 1971, pp. 265-271). | MR 45 #268 | Zbl 0246.22017
and ,[AVE] Orbits of greatest dimension in semisimple linear Lie groups (Functional Anal. Appl., Vol. 1, 1967, pp. 257-261). | Zbl 0176.30301
, and ,[BGG] Differential operators on the cubic cone (Russian Math. Surveys, Vol. 27, 1972, pp. 169-174). | MR 52 #6024 | Zbl 0257.58010
, and ,[Bj] Rings of Differential Operators, North-Holland, Amsterdam, 1979. | Zbl 0499.13009
,[Br] Sur les modules de covariants (Ann. Sci. École Norm. Sup., Vol. 26, 1993, pp. 1-21). | Numdam | MR 95c:14062 | Zbl 0781.13002
,[BE] What makes a complex exact ? (Jour. of Alg., Vol. 25, 1973, pp. 259-268). | MR 47 #3369 | Zbl 0264.13007
and ,[D] Topics in Local Algebra, Notre Dame Mathematical Lectures No. 10, University of Notre Dame Press, 1967. | MR 39 #2748 | Zbl 0193.00101
,[El1] Canonical form and stationary subalgebras of points of general position for simple linear Lie groups (Functional Anal. Appl., Vol. 6, 1972, pp. 44-53). | MR 46 #3689 | Zbl 0252.22015
,[El2] Stationary subalgebras of points of the common state for irreducible linear Lie groups (Functional Anal. Appl., Vol. 6, 1972, pp. 139-148). | Zbl 0252.22016
,[Go] Coranks of elements of linear groups and the complexity of algebras of invariants (Leningrad Math. J., Vol. 2, 1991, pp. 245-267). | MR 91h:20063 | Zbl 0717.20032
,[Gr1] Torsion homologique et sections rationnelles, Séminaire Chevalley 1958, exposé n° 5. | Numdam
,[Gr2] Éléments de Géométrie Algébrique : Étude locale des schémas et des morphismes de schémas (Publ. Math. IHES, Vol. 32, 1967, pp. 1-361). | Numdam | MR 39 #220 | Zbl 0153.22301
,[HS] A course in Homological Algebra, Graduate Texts in Mathematics 4, Springer-Verlag, New York, 1971. | MR 49 #10751 | Zbl 0238.18006
and ,[Ho] Remarks on classical invariant theory (Trans. AMS, Vol. 313, 1989, pp. 539-570). | MR 90h:22015a | Zbl 0674.15021
,[Ish] Nakai's conjecture for invariant subrings (Hiroshima Math. J., Vol. 15, 1985, pp. 429-436). | MR 87b:13003 | Zbl 0586.13019
,[Ka] Formes et opérateurs différentiels sur les espaces analytiques complexes (Bull. Soc. Math. France, Mémoire, Vol. 53, 1977, pp. 5-80). | Numdam | MR 58 #6332 | Zbl 0376.32001
,[Ke] Some quotient surfaces are smooth (Mich. Math. Jour., Vol. 27, 1980, pp. 295-299). | MR 81m:14009 | Zbl 0465.14018
,[Kn] Über die Glattheit von Quotientenabbildungen (Manuscripta Math., Vol. 56, 1986, pp. 410-427). | MR 88f:14041 | Zbl 0585.14033
,[Kr1] Geometrische Methoden in der Invariantentheorie, Vieweg-Verlag, Braunschweig, 1985. | Zbl 0669.14003
,[Kr2] G-vector bundles and the linearization problem (Group Actions and Invariant Theory, Can. Math. Soc. Conf. Proc., Vol. 10, 1989, pp. 111-123). | MR 90j:14062 | Zbl 0703.14009
,[Le1] Anneaux d'opérateurs différentiels, Séminaire Dubreil-Malliavin (1980) (Lecture Notes in Mathematics, Vol. 867, 1981, pp. 157-173). | MR 84j:32009 | Zbl 0507.14012
,[Le2] Relèvements d'opérateurs différentiels sur les anneaux d'invariants, Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory (Progress in Mathematics, Vol. 92, Birkhäuser, Boston, 1990, pp. 449-470). | MR 92f:16033 | Zbl 0733.16009
,[LS] Rings of differential operators on classical rings of invariants (Memoirs of the AMS, Vol. 412, 1989). | MR 90i:17018 | Zbl 0691.16019
and ,[Li] Koreguläre und äquidimensionale Darstellungen (Jour. of Alg. Vol. 123, 1989, pp. 193-222). | MR 90e:20039 | Zbl 0688.14042
,[Lu1] Slices étales (Bull. Soc. Math. France, Mémoire, Vol. 33, 1973, pp. 81-105). | Numdam | MR 49 #7269 | Zbl 0286.14014
,[Lu2] Adhérences d'orbite et invariants (Invent. Math., Vol. 29, 1975, pp. 231-238). | MR 51 #12879 | Zbl 0315.14018
,[LR] A generalization of the Chevalley restriction theorem (Duke Math. J., Vol. 46, 1979, pp. 487-496). | MR 80k:14049 | Zbl 0444.14010
and ,[Ma] Commutative Algebra, Second Edition, Benjamin/Cummings, 1980. | MR 82i:13003 | Zbl 0441.13001
,[MR] Noncommutative Noetherian Rings, Wiley, New York, 1987. | MR 89j:16023 | Zbl 0644.16008
and ,[MumF] Geometric Invariant Theory, 2nd edn., Springer Verlag, New York, 1982. | Zbl 0504.14008
and ,[Mu] Rings of differential operators on invariant rings of tori (Trans. Amer. Math. Soc., Vol. 303, 1987, pp. 805-827). | MR 88m:32019 | Zbl 0628.13019
,[Po1] Stability criteria for the action of a semi-simple group on a factorial manifold (Math. USSR-Izvestija, Vol. 4, 1970, pp. 527-535). | Zbl 0261.14011
,[Po2] A finiteness theorem for representations with a free algebra of invariants (Math. USSR-Izv., Vol. 20, 1983, pp. 333-354). | Zbl 0547.20034
,[PS] Inequalities defining orbit spaces (Inv. Math., Vol. 81, 1985, pp. 539-554). | MR 87h:20078 | Zbl 0578.14010
and ,[Re] Affine domains of finite Gelfand-Kirillov dimension which are right, but not left, noetherian (Bull. London Math. Soc., Vol. 16, 1984, pp. 590-594). | MR 85k:16047 | Zbl 0547.16007
,[S1] Representations of simple groups with a regular ring of invariants (Invent. Math., Vol. 49, 1978, pp. 167-191). | MR 80m:14032 | Zbl 0391.20032
,[S2] Representations of simple Lie groups with a free module of covariants (Invent. Math., Vol. 50, 1978, pp. 1-12). | MR 80c:14008 | Zbl 0391.20033
,[S3] Lifting smooth homotopies of orbit spaces (Publ. Math. IHES, Vol. 51, 1980, pp. 37-135). | Numdam | MR 81h:57024 | Zbl 0449.57009
,[S4] Invariant theory of G2 and Spin7 (Comment. Math. Helv., Vol. 63, 1988, pp. 624-663). | MR 89k:14080 | Zbl 0664.14006
,[S5] Exotic algebraic group actions (C. R. Acad. Sci. Paris, Vol. 309, 1989, pp. 89-94). | MR 91b:14066 | Zbl 0688.14040
,[S6] Differential operators and orbit spaces, Proceedings of the Hyderabad Conference on Algebraic Groups, Manoj Prakashan, Madras, 1991, pp. 509-516. | MR 1131325 | Zbl 0844.14021
,[S7] Differential operators on quotients of simple groups, Jour. of Alg., Vol. 169, 1994, pp. 248-273. | MR 95i:16027 | Zbl 0835.14019
,[Se] Algèbre Locale. Multiplicités, Lecture Notes in Mathematics, No. 11, Springer-Verlag, New York, 1965. | MR 34 #1352 | Zbl 0142.28603
,[Sl] Der Scheibensatz für algebraische Transformationsgruppen, Algebraic Transformation Groups and Invariant Theory, DMV Seminar, Vol. 13, Birkhäuser Verlag, Basel-Boston, 1989, pp. 89-113. | MR 1044587 | Zbl 0722.14031
,[SmSt] Differential operators on an affine curve (Proc. London Math. Soc., Vol. 56, 1988, pp. 229-259). | MR 89d:14039 | Zbl 0672.14017
and ,[Sw] Groups of simple algebras (Publ. Math. IHES, Vol. 44, 1974, pp. 79-190). | Numdam | MR 51 #587 | Zbl 0314.16008
,[VdB] Differential operators on semi-invariants for tori and weighted projective spaces, Séminaire Malliavin (1990) (Lecture Notes in Mathematics, Vol. 1478, 1992, pp. 255-272). | MR 93h:16046 | Zbl 0802.13005
,[Vi] Complexity of actions of reductive groups (Functional Anal. Appl. Vol. 20, 1986, pp. 1-11). | MR 87j:14077 | Zbl 0601.14038
,[We] Some recent results on the Popov conjecture, Group Actions and Invariant Theory, CMS Conference Proceedings, Vol. 10, 1989, pp. 221-228. | MR 90m:14044 | Zbl 0746.20023
,[Weyl] The Classical Groups, 2nd ed., Princeton University Press, Princeton, 1946.
,