zbMATH — the first resource for mathematics

Representations of simple Lie groups with a free module of covariants. (English) Zbl 0391.20033

20G05 Representation theory for linear algebraic groups
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
15A72 Vector and tensor algebra, theory of invariants
Full Text: DOI EuDML
[1] Bourbaki, N.: Algèbre, 3rd edn., Paris: Hermann, 1962 · Zbl 0142.00102
[2] Dieudonné, J., Carrell, J.: Invariant theory, old and new. Adv. in Math.4, 1-80 (1970) · Zbl 0196.05802 · doi:10.1016/0001-8708(70)90015-0
[3] Élashvili, A.G.: Canonical form and stationary subalgebras of points of general position for simple linear Lie groups. Functional Anal. Appl.6, 44-53 (1972) · Zbl 0252.22015 · doi:10.1007/BF01075509
[4] Grothendieck, A.: Cohomologie Locale des Faisceaux et Théorèmes de Lefschetz Locaux et Globaux (SGA 2), Amsterdam: North Holland, 1968 · Zbl 0197.47202
[5] Gurevich, G.B.: Foundations of the Theory of Algebraic Invariants, Groningen: Noordhoff, 1964 · Zbl 0128.24601
[6] Hsiang, W.C., Hsiang, W.Y.: Differentiable actions of compact connected classical groups: II. Ann. of Math.92, 189-223 (1970) · Zbl 0205.53902 · doi:10.2307/1970834
[7] Igusa, J.-I.: Geometry of absolutely admissible representations. In: Number Theory, Algebraic Geometry and Commutative Algebra, pp. 373-452. Tokyo: Kinokuniya, 1973
[8] Kac, V.G., Popov, V.L., Vinberg, É.B.: Sur les groupes linéaires algébriques dont l’algèbre des invariants est libre. C.R. Acad. Sci. Paris283, 875-878 (1976) · Zbl 0343.20023
[9] Kostant, B.: Lie group representations on polynomial rings. Amer. J. Math.85, 327-402 (1963) · Zbl 0124.26802 · doi:10.2307/2373130
[10] Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoire33, 81-105 (1973) · Zbl 0286.14014
[11] Luna, D.: Adhérences d’orbite et invariants, Invent. Math.29, 231-238 (1975) · Zbl 0315.14018 · doi:10.1007/BF01389851
[12] Mumford, D.: Geometric Invariant Theory, Erg. der Math. Bd. 34, New York: Springer-Verlag 1965 · Zbl 0147.39304
[13] Popov, A.M.: Irreducible simple linear Lie groups with finite standard subgroups of general position. Functional Anal. Appl.9, 346-347 (1976) · Zbl 0339.22007 · doi:10.1007/BF01075890
[14] Popov, V.L.: Representations with a free module of covariants. Functional Anal. Appl.10, 242-244 (1977) · Zbl 0365.20053 · doi:10.1007/BF01075538
[15] Rallis, S.: New and old results in invariant theory with applications to arithmetic groups. In: Symmetric Spaces, pp. 443-458. New York: Marcel Dekker, 1972 · Zbl 0237.20042
[16] Schwarz, G.W.: Lifting smooth homotopies of orbit spaces. To appear in Inst. Hautes Études Sci. Publ. Math. · Zbl 0449.57009
[17] Schwarz, G.W.: Representations of simple Lie groups with regular rings of invariants. Inv. Math.49, 167-191 (1978) · Zbl 0391.20032 · doi:10.1007/BF01403085
[18] Serre, J.-P.: Algèbre Locale-Multiplicités, Lecture Notes in Mathematics No. 11, New York: Springer-Verlag, 1965
[19] Weyl, H.: The Classical Groups, 2nd edn., Princeton: Princeton University Press, 1946 · Zbl 1024.20502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.