Lifting differential operators from orbit spaces

Schwarz, Gerald W.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 28 (1995) no. 3, pp. 253-305.

[AP] E. Andreev and V. Popov, 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 | Zbl

[AVE] E. Andreev, E. Vinberg and A. Elashvili, Orbits of greatest dimension in semisimple linear Lie groups (Functional Anal. Appl., Vol. 1, 1967, pp. 257-261). | Zbl

[BGG] I. N. Bernstein, I. M. Gel'Fand and S. I. Gel'Fand, Differential operators on the cubic cone (Russian Math. Surveys, Vol. 27, 1972, pp. 169-174). | MR | Zbl

[Bj] J.-E. Björk, Rings of Differential Operators, North-Holland, Amsterdam, 1979. | Zbl

[Br] M. Brion, Sur les modules de covariants (Ann. Sci. École Norm. Sup., Vol. 26, 1993, pp. 1-21). | Numdam | MR | Zbl

[BE] D. Buchsbaum and D. Eisenbud, What makes a complex exact ? (Jour. of Alg., Vol. 25, 1973, pp. 259-268). | MR | Zbl

[D] J. Dieudonné, Topics in Local Algebra, Notre Dame Mathematical Lectures No. 10, University of Notre Dame Press, 1967. | MR | Zbl

[El1] A. Elashvili, 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 | Zbl

[El2] A. Elashvili, Stationary subalgebras of points of the common state for irreducible linear Lie groups (Functional Anal. Appl., Vol. 6, 1972, pp. 139-148). | Zbl

[Go] N. Gordeev, Coranks of elements of linear groups and the complexity of algebras of invariants (Leningrad Math. J., Vol. 2, 1991, pp. 245-267). | MR | Zbl

[Gr1] A. Grothendieck, Torsion homologique et sections rationnelles, Séminaire Chevalley 1958, exposé n° 5. | Numdam

[Gr2] A. Grothendieck, Éléments de Géométrie Algébrique : Étude locale des schémas et des morphismes de schémas (Publ. Math. IHES, Vol. 32, 1967, pp. 1-361). | Numdam | MR | Zbl

[HS] P. J. Hilton and U. Stammbach, A course in Homological Algebra, Graduate Texts in Mathematics 4, Springer-Verlag, New York, 1971. | MR | Zbl

[Ho] R. Howe, Remarks on classical invariant theory (Trans. AMS, Vol. 313, 1989, pp. 539-570). | MR | Zbl

[Ish] Y. Ishibashi, Nakai's conjecture for invariant subrings (Hiroshima Math. J., Vol. 15, 1985, pp. 429-436). | MR | Zbl

[Ka] J.-M. Kantor, Formes et opérateurs différentiels sur les espaces analytiques complexes (Bull. Soc. Math. France, Mémoire, Vol. 53, 1977, pp. 5-80). | Numdam | MR | Zbl

[Ke] G. Kempf, Some quotient surfaces are smooth (Mich. Math. Jour., Vol. 27, 1980, pp. 295-299). | MR | Zbl

[Kn] F. Knop, Über die Glattheit von Quotientenabbildungen (Manuscripta Math., Vol. 56, 1986, pp. 410-427). | MR | Zbl

[Kr1] H. Kraft, Geometrische Methoden in der Invariantentheorie, Vieweg-Verlag, Braunschweig, 1985. | Zbl

[Kr2] H. Kraft, G-vector bundles and the linearization problem (Group Actions and Invariant Theory, Can. Math. Soc. Conf. Proc., Vol. 10, 1989, pp. 111-123). | MR | Zbl

[Le1] T. Levasseur, Anneaux d'opérateurs différentiels, Séminaire Dubreil-Malliavin (1980) (Lecture Notes in Mathematics, Vol. 867, 1981, pp. 157-173). | MR | Zbl

[Le2] T. Levasseur, 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 | Zbl

[LS] T. Levasseur and J. T. Stafford, Rings of differential operators on classical rings of invariants (Memoirs of the AMS, Vol. 412, 1989). | MR | Zbl

[Li] P. Littelmann, Koreguläre und äquidimensionale Darstellungen (Jour. of Alg. Vol. 123, 1989, pp. 193-222). | MR | Zbl

[Lu1] D. Luna, Slices étales (Bull. Soc. Math. France, Mémoire, Vol. 33, 1973, pp. 81-105). | Numdam | MR | Zbl

[Lu2] D. Luna, Adhérences d'orbite et invariants (Invent. Math., Vol. 29, 1975, pp. 231-238). | MR | Zbl

[LR] D. Luna and R. W. Richardson, A generalization of the Chevalley restriction theorem (Duke Math. J., Vol. 46, 1979, pp. 487-496). | MR | Zbl

[Ma] H. Matsumura, Commutative Algebra, Second Edition, Benjamin/Cummings, 1980. | MR | Zbl

[MR] J. C. Mcconnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley, New York, 1987. | MR | Zbl

[MumF] D. Mumford and J. Fogarty, Geometric Invariant Theory, 2nd edn., Springer Verlag, New York, 1982. | Zbl

[Mu] I. Musson, Rings of differential operators on invariant rings of tori (Trans. Amer. Math. Soc., Vol. 303, 1987, pp. 805-827). | MR | Zbl

[Po1] V. Popov, Stability criteria for the action of a semi-simple group on a factorial manifold (Math. USSR-Izvestija, Vol. 4, 1970, pp. 527-535). | Zbl

[Po2] V. Popov, A finiteness theorem for representations with a free algebra of invariants (Math. USSR-Izv., Vol. 20, 1983, pp. 333-354). | Zbl

[PS] C. Procesi and G. Schwarz, Inequalities defining orbit spaces (Inv. Math., Vol. 81, 1985, pp. 539-554). | MR | Zbl

[Re] R. Resco, 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 | Zbl

[S1] G. Schwarz, Representations of simple groups with a regular ring of invariants (Invent. Math., Vol. 49, 1978, pp. 167-191). | MR | Zbl

[S2] G. Schwarz, Representations of simple Lie groups with a free module of covariants (Invent. Math., Vol. 50, 1978, pp. 1-12). | MR | Zbl

[S3] G. Schwarz, Lifting smooth homotopies of orbit spaces (Publ. Math. IHES, Vol. 51, 1980, pp. 37-135). | Numdam | MR | Zbl

[S4] G. Schwarz, Invariant theory of G2 and Spin7 (Comment. Math. Helv., Vol. 63, 1988, pp. 624-663). | MR | Zbl

[S5] G. Schwarz, Exotic algebraic group actions (C. R. Acad. Sci. Paris, Vol. 309, 1989, pp. 89-94). | MR | Zbl

[S6] G. Schwarz, Differential operators and orbit spaces, Proceedings of the Hyderabad Conference on Algebraic Groups, Manoj Prakashan, Madras, 1991, pp. 509-516. | MR | Zbl

[S7] G. Schwarz, Differential operators on quotients of simple groups, Jour. of Alg., Vol. 169, 1994, pp. 248-273. | MR | Zbl

[Se] J.-P. Serre, Algèbre Locale. Multiplicités, Lecture Notes in Mathematics, No. 11, Springer-Verlag, New York, 1965. | MR | Zbl

[Sl] P. Slodowy, Der Scheibensatz für algebraische Transformationsgruppen, Algebraic Transformation Groups and Invariant Theory, DMV Seminar, Vol. 13, Birkhäuser Verlag, Basel-Boston, 1989, pp. 89-113. | MR | Zbl

[SmSt] S. P. Smith and J. T. Stafford, Differential operators on an affine curve (Proc. London Math. Soc., Vol. 56, 1988, pp. 229-259). | MR | Zbl

[Sw] M. E. Sweedler, Groups of simple algebras (Publ. Math. IHES, Vol. 44, 1974, pp. 79-190). | Numdam | MR | Zbl

[VdB] M. Van Den Bergh, 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 | Zbl

[Vi] E. B. Vinberg, Complexity of actions of reductive groups (Functional Anal. Appl. Vol. 20, 1986, pp. 1-11). | MR | Zbl

[We] D. Wehlau, Some recent results on the Popov conjecture, Group Actions and Invariant Theory, CMS Conference Proceedings, Vol. 10, 1989, pp. 221-228. | MR | Zbl

[Weyl] H. Weyl, The Classical Groups, 2nd ed., Princeton University Press, Princeton, 1946.