Lifting differential operators from orbit spaces
Annales scientifiques de l'École Normale Supérieure (1995)
- Volume: 28, Issue: 3, page 253-305
- ISSN: 0012-9593
Access Full Article
topHow to cite
topSchwarz, Gerald W.. "Lifting differential operators from orbit spaces." Annales scientifiques de l'École Normale Supérieure 28.3 (1995): 253-305. <http://eudml.org/doc/82383>.
@article{Schwarz1995,
author = {Schwarz, Gerald W.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {quotient spaces; algebraic differential operator},
language = {eng},
number = {3},
pages = {253-305},
publisher = {Elsevier},
title = {Lifting differential operators from orbit spaces},
url = {http://eudml.org/doc/82383},
volume = {28},
year = {1995},
}
TY - JOUR
AU - Schwarz, Gerald W.
TI - Lifting differential operators from orbit spaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1995
PB - Elsevier
VL - 28
IS - 3
SP - 253
EP - 305
LA - eng
KW - quotient spaces; algebraic differential operator
UR - http://eudml.org/doc/82383
ER -
References
top- [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). Zbl0246.22017MR45 #268
- [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). Zbl0176.30301
- [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). Zbl0257.58010MR52 #6024
- [Bj] J.-E. BJÖRK, Rings of Differential Operators, North-Holland, Amsterdam, 1979. Zbl0499.13009
- [Br] M. BRION, Sur les modules de covariants (Ann. Sci. École Norm. Sup., Vol. 26, 1993, pp. 1-21). Zbl0781.13002MR95c:14062
- [BE] D. BUCHSBAUM and D. EISENBUD, What makes a complex exact ? (Jour. of Alg., Vol. 25, 1973, pp. 259-268). Zbl0264.13007MR47 #3369
- [D] J. DIEUDONNÉ, Topics in Local Algebra, Notre Dame Mathematical Lectures No. 10, University of Notre Dame Press, 1967. Zbl0193.00101MR39 #2748
- [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). Zbl0252.22015MR46 #3689
- [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). Zbl0252.22016
- [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). Zbl0717.20032MR91h:20063
- [Gr1] A. GROTHENDIECK, Torsion homologique et sections rationnelles, Séminaire Chevalley 1958, exposé n° 5.
- [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). Zbl0153.22301MR39 #220
- [HS] P. J. HILTON and U. STAMMBACH, A course in Homological Algebra, Graduate Texts in Mathematics 4, Springer-Verlag, New York, 1971. Zbl0238.18006MR49 #10751
- [Ho] R. HOWE, Remarks on classical invariant theory (Trans. AMS, Vol. 313, 1989, pp. 539-570). Zbl0674.15021MR90h:22015a
- [Ish] Y. ISHIBASHI, Nakai's conjecture for invariant subrings (Hiroshima Math. J., Vol. 15, 1985, pp. 429-436). Zbl0586.13019MR87b:13003
- [Ka] J.-M. KANTOR, Formes et opérateurs différentiels sur les espaces analytiques complexes (Bull. Soc. Math. France, Mémoire, Vol. 53, 1977, pp. 5-80). Zbl0376.32001MR58 #6332
- [Ke] G. KEMPF, Some quotient surfaces are smooth (Mich. Math. Jour., Vol. 27, 1980, pp. 295-299). Zbl0465.14018MR81m:14009
- [Kn] F. KNOP, Über die Glattheit von Quotientenabbildungen (Manuscripta Math., Vol. 56, 1986, pp. 410-427). Zbl0585.14033MR88f:14041
- [Kr1] H. KRAFT, Geometrische Methoden in der Invariantentheorie, Vieweg-Verlag, Braunschweig, 1985. Zbl0669.14003
- [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). Zbl0703.14009MR90j:14062
- [Le1] T. LEVASSEUR, Anneaux d'opérateurs différentiels, Séminaire Dubreil-Malliavin (1980) (Lecture Notes in Mathematics, Vol. 867, 1981, pp. 157-173). Zbl0507.14012MR84j:32009
- [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). Zbl0733.16009MR92f:16033
- [LS] T. LEVASSEUR and J. T. STAFFORD, Rings of differential operators on classical rings of invariants (Memoirs of the AMS, Vol. 412, 1989). Zbl0691.16019MR90i:17018
- [Li] P. LITTELMANN, Koreguläre und äquidimensionale Darstellungen (Jour. of Alg. Vol. 123, 1989, pp. 193-222). Zbl0688.14042MR90e:20039
- [Lu1] D. LUNA, Slices étales (Bull. Soc. Math. France, Mémoire, Vol. 33, 1973, pp. 81-105). Zbl0286.14014MR49 #7269
- [Lu2] D. LUNA, Adhérences d'orbite et invariants (Invent. Math., Vol. 29, 1975, pp. 231-238). Zbl0315.14018MR51 #12879
- [LR] D. LUNA and R. W. RICHARDSON, A generalization of the Chevalley restriction theorem (Duke Math. J., Vol. 46, 1979, pp. 487-496). Zbl0444.14010MR80k:14049
- [Ma] H. MATSUMURA, Commutative Algebra, Second Edition, Benjamin/Cummings, 1980. Zbl0441.13001MR82i:13003
- [MR] J. C. MCCONNELL and J. C. ROBSON, Noncommutative Noetherian Rings, Wiley, New York, 1987. Zbl0644.16008MR89j:16023
- [MumF] D. MUMFORD and J. FOGARTY, Geometric Invariant Theory, 2nd edn., Springer Verlag, New York, 1982. Zbl0504.14008
- [Mu] I. MUSSON, Rings of differential operators on invariant rings of tori (Trans. Amer. Math. Soc., Vol. 303, 1987, pp. 805-827). Zbl0628.13019MR88m:32019
- [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). Zbl0261.14011
- [Po2] V. POPOV, A finiteness theorem for representations with a free algebra of invariants (Math. USSR-Izv., Vol. 20, 1983, pp. 333-354). Zbl0547.20034
- [PS] C. PROCESI and G. SCHWARZ, Inequalities defining orbit spaces (Inv. Math., Vol. 81, 1985, pp. 539-554). Zbl0578.14010MR87h:20078
- [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). Zbl0547.16007MR85k:16047
- [S1] G. SCHWARZ, Representations of simple groups with a regular ring of invariants (Invent. Math., Vol. 49, 1978, pp. 167-191). Zbl0391.20032MR80m:14032
- [S2] G. SCHWARZ, Representations of simple Lie groups with a free module of covariants (Invent. Math., Vol. 50, 1978, pp. 1-12). Zbl0391.20033MR80c:14008
- [S3] G. SCHWARZ, Lifting smooth homotopies of orbit spaces (Publ. Math. IHES, Vol. 51, 1980, pp. 37-135). Zbl0449.57009MR81h:57024
- [S4] G. SCHWARZ, Invariant theory of G2 and Spin7 (Comment. Math. Helv., Vol. 63, 1988, pp. 624-663). Zbl0664.14006MR89k:14080
- [S5] G. SCHWARZ, Exotic algebraic group actions (C. R. Acad. Sci. Paris, Vol. 309, 1989, pp. 89-94). Zbl0688.14040MR91b:14066
- [S6] G. SCHWARZ, Differential operators and orbit spaces, Proceedings of the Hyderabad Conference on Algebraic Groups, Manoj Prakashan, Madras, 1991, pp. 509-516. Zbl0844.14021MR1131325
- [S7] G. SCHWARZ, Differential operators on quotients of simple groups, Jour. of Alg., Vol. 169, 1994, pp. 248-273. Zbl0835.14019MR95i:16027
- [Se] J.-P. SERRE, Algèbre Locale. Multiplicités, Lecture Notes in Mathematics, No. 11, Springer-Verlag, New York, 1965. Zbl0142.28603MR34 #1352
- [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. Zbl0722.14031MR1044587
- [SmSt] S. P. SMITH and J. T. STAFFORD, Differential operators on an affine curve (Proc. London Math. Soc., Vol. 56, 1988, pp. 229-259). Zbl0672.14017MR89d:14039
- [Sw] M. E. SWEEDLER, Groups of simple algebras (Publ. Math. IHES, Vol. 44, 1974, pp. 79-190). Zbl0314.16008MR51 #587
- [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). Zbl0802.13005MR93h:16046
- [Vi] E. B. VINBERG, Complexity of actions of reductive groups (Functional Anal. Appl. Vol. 20, 1986, pp. 1-11). Zbl0601.14038MR87j:14077
- [We] D. WEHLAU, Some recent results on the Popov conjecture, Group Actions and Invariant Theory, CMS Conference Proceedings, Vol. 10, 1989, pp. 221-228. Zbl0746.20023MR90m:14044
- [Weyl] H. WEYL, The Classical Groups, 2nd ed., Princeton University Press, Princeton, 1946. Zbl1024.20502
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.