×

zbMATH — the first resource for mathematics

Closures of conjugacy classes of matrices are normal. (English) Zbl 0434.14026

MSC:
14L30 Group actions on varieties or schemes (quotients)
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14M10 Complete intersections
14B05 Singularities in algebraic geometry
20G05 Representation theory for linear algebraic groups
15A21 Canonical forms, reductions, classification
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Borho, W., Kraft, H.: Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. Helv.54, 61-104 (1979) · Zbl 0395.14013 · doi:10.1007/BF02566256
[2] De Concini, C., Procesi, C.: A characteristic free approach to invariant theory. Adv. Math.21, 330-354 (1976) · Zbl 0347.20025 · doi:10.1016/S0001-8708(76)80003-5
[3] Donovan, P., Freislich, M.R.: The representation theory of finite graphs and associated algebras. Carleton Lecture Notes5 (1973) · Zbl 0304.08006
[4] Elkik, R.: Désingularisation des adhérences d’orbites polarisables et des nappes dans les algèbres de Lie réductives. Preprint.
[5] Gabriel, P.: Représentations indécomposables. Seminaire Bourbaki exp.444, Springer Lecture Notes431 (1975)
[6] Grothendieck, A., Dieudonné, J.: EGA O-IV. Publ. Math. de l’I.H.E.S.11, 20, 24, 32; Paris (1961-1967)
[7] Hesselink, W.: Singularities in the nilpotent scheme of a classical group. Trans. Am. Math. Soc.222, 1-32 (1976) · Zbl 0332.14017 · doi:10.1090/S0002-9947-1976-0429875-8
[8] Hesselink, W.: Closure of orbits in a Lie algebra. Comment. Math. Helv.54, 105-110 (1979) · Zbl 0395.14014 · doi:10.1007/BF02566258
[9] Kempf, G., Knudsen, F., Mumford, D., Saint-Donat, B.: Toroidal Embeddings I. Springer Lecture Notes339 (1973) · Zbl 0271.14017
[10] Kostant, B.: A theorem of Frobenius, a theorem of Amitsur-Levitzki and cohomology theory. J. Math. Mech.7, 237-264 (1958) · Zbl 0087.25702
[11] Kostant, B.: Lie group representations on polynomial rings. Am. J. Math.86, 327-402 (1963) · Zbl 0124.26802 · doi:10.2307/2373130
[12] Kostant, B., Rallis, S.: Orbits and representations associated with symmetric spaces. Am. J. Math.93, 753-809 (1971) · Zbl 0224.22013 · doi:10.2307/2373470
[13] Kraft, H.: Parametrisierung von Konjugationsklassen in \(\mathfrak{s}\mathfrak{l}_n \) . Math. Ann.234, 209-220 (1978) · Zbl 0369.17003 · doi:10.1007/BF01420644
[14] Nazarova, L.A.: Representations of quivers of infinite type. Akad. Nauk. SSSR37, 752-791 (1973) · Zbl 0298.15012
[15] Procesi, C.: The invariant theory ofn\(\times\)n matrices. Adv. Math.19 306-381 (1976) · Zbl 0331.15021 · doi:10.1016/0001-8708(76)90027-X
[16] Sibirskii, K.S.: On unitary and orthogonal matrix invariants. Dokl. Akad. Nauk SSSR172 no 1 (1967)
[17] Vinberg, E.B.: The Weyl group of a graded Lie algebra. Izv. Akad. Nauk SSSR40, no 3 (1976) · Zbl 0363.20035
[18] Weyl, H.: Classical groups. Princeton Math. Series1 (1946) · Zbl 1024.20502
[19] Loupias, M.: Représentations indécomposables de dimension finie des algèbres de Lie. Manuscripta math.6, 365-379 (1972) · Zbl 0229.17006 · doi:10.1007/BF01303689
[20] Mumford, D.: Geometric Invariant Theory. Erg. der Math.34, Berlin-Heidelberg-New York: Springer Verlag 1970 · Zbl 0147.39304
[21] Demazure, M.: Démonstration de la conjecture de Mumford (d’après W. Haboush). Sém. Bourbaki 74/75, exp.462. Berlin-Heidelberg-New York: Springer Verlag, Lecture Notes514 (1976) · Zbl 0351.14027
[22] Vust, Th.: Sur la théorie des invariants des groupes classiques. Ann. Inst. Fourier26, 1-31 (1976) · Zbl 0314.20035
[23] Procesi, C., Kraft, H.: Classi coniugati inGL(n),?. Rend. Sem. mat. Univ. Roma (1979)
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.