This is a preview of subscription content, log in via an institution to check access.
References
Andreev, E.M., Vinberg, E.B., Elashvili, A.G.: Orbits of greatest dimension of semisimple linear Lie groups, Functional Anal. Appl.1, 257–261 (1967)
Bernstein, I.N., Gelfand, I.M., Ponomarev, V.A.: Coxeter functors and Gabriel's theorem, Russian Math. Surveys28, 17–32 (1973)
Brenner, S.: Quivers with commutativity conditions and some phenomenology of forms, Lecture Notes in Math.,488, 29–53 (1975)
De Concini, C., Procesi, C.: Characteristic free approach to Invariant theory, Advances in Math.21, 330–354 (1976)
Dlab, V., Ringel, C.M.: Indecomposable representations of graphs and algebras, Memoirs of Amer. Math. Soc. 6 no.173, 1–57 (1976)
Duflo, M.: Parametrisation of the set of regular orbits of the coadjoint representation of a Lie group, preprint (1978)
Elashvili, A.G.: Stabilizers of points in general position for irreducible linear Lie groups, Functional Anal. Appl.6, 165–178 (1972)
Gabriel, P.: Unzerlegbare Darstellungen I., Man. Math.6, 71–103 (1972)
Gabriel, P.: Indecomposable representations II, Symposia Math. Inst. Naz. Alta Mat.,XI, 81–104 (1973)
Hsiang, W.C., Hsiang, W.Y.: Differentiable action of compact connected classical groups II, Ann. of Math.92, 189–223 (1970)
Kac, V.G.: Simple irreducible graded Lie algebras of finite growth, Math. USSR Izvestija2, 1271–1311 (1968)
Kac, V.G.: Infinite dimensional Lie algebras and the Dedekind η-function. Functional Anal. Appl.8, 68–70 (1974)
Kac, V.G.: Conserning the question of describing the orbit space of a linear algebraic group, Uspechi Mat. Nauk30, 173–174 (1975) (in Russian)
Kac, V.G., Popov, V.L., Vinberg, E.B.: Sur les groupes linéares algébrique dont l'algebre des invariants est libre. C.R. Acad. Sci, Paris283, 865–878 (1976)
Kac, V.G.: Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula, Advances in Math.,30, 85–136 (1978)
Gatti, V., Viniberghi, E.: Spinors of 13-dimensional space, Advances in Math.30, 137–155 (1978)
Luna, D.: Adhérences d'orbite et invariants. Invent. Math.29, 231–238 (1975)
Moody, R.V.: Root systems of hyperbolic type, preprint
Nazarova, L.A.: Representations of quivers of infinite type, Math USSR, Izvestija, Ser. Mat.7, 752–791 (1973)
Pyasetskii, V.: Linear Lie groups acting with finitely many orbits, Functional Anal. Appl.9, 351–353 (1975)
Richardson, R.W.: Deformations of Lie subgroups and the variation of isotrophy subgroups. Acta Math,129, 35–73 (1972)
Ringel, C.M.: Representations ofK-species and bimodules. J. of Algebra,41, 269–302 (1976)
Rosenlicht: A remark on quotient spaces, An. Acad. Brasil cienc.35, 487–489 (1963)
Sato, M., Kimura, T.: A classification of irreducible prehomogeneous vector spaces and their relative invariants. Nagoya Math. J.65, 1–155 (1977)
Vinberg, E.B.: Discrete linear groups generated by reflections, Math. USSR, Izvestija, Ser. Mat.5, 1083–1119 (1971)
Kronecker, L.: Algebraishe Reduction der Schaaren bilinearer Formen, 763–776. Berlin: S.-B. Akad. 1890
Thrall, R., Chanler, J.: Ternary trilinear forms in the field of complex numbers, Duke Math. J.4, 678–690 (1938)
Thrall, R.: On projective equivalence of trilinear forms, Ann. Math.42, 469–485 (1941)
Author information
Authors and Affiliations
Additional information
Partially supported by NSF grant MCS 7609177
Rights and permissions
About this article
Cite this article
Kac, V.G. Infinite root systems, representations of graphs and invariant theory. Invent Math 56, 57–92 (1980). https://doi.org/10.1007/BF01403155
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01403155