Quelques résultats de finitude en théorie des invariants

Jacques Dixmier

Séminaire Bourbaki (1985-1986)

  • Volume: 28, page 163-175
  • ISSN: 0303-1179

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Dixmier, Jacques. "Quelques résultats de finitude en théorie des invariants." Séminaire Bourbaki 28 (1985-1986): 163-175. <http://eudml.org/doc/110059>.

@article{Dixmier1985-1986,
author = {Dixmier, Jacques},
journal = {Séminaire Bourbaki},
keywords = {connected semisimple algebraic group; finite-dimensional rational G- modules; algebra of invariants; homological dimension},
language = {fre},
pages = {163-175},
publisher = {Société Mathématique de France},
title = {Quelques résultats de finitude en théorie des invariants},
url = {http://eudml.org/doc/110059},
volume = {28},
year = {1985-1986},
}

TY - JOUR
AU - Dixmier, Jacques
TI - Quelques résultats de finitude en théorie des invariants
JO - Séminaire Bourbaki
PY - 1985-1986
PB - Société Mathématique de France
VL - 28
SP - 163
EP - 175
LA - fre
KW - connected semisimple algebraic group; finite-dimensional rational G- modules; algebra of invariants; homological dimension
UR - http://eudml.org/doc/110059
ER -

References

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  1. [1] O.M. Adamovich and E.M. Golovina - Simple linear Lie groups having a free algebra of invariants, Questions in group theory and homological algebra, Vyp. 2, Izdat. Yaroslav Gos. Univ., Yaroslav, 1979, 3-41. Zbl0446.22017MR742478
  2. [2] E.M. Andreev and V.L. Popov - On stationary subgroups of points in general position in the representation space of a semisimple Lie group, Funktsional Anal. i Prilozhen, 5, 1971, 1-8. Zbl0246.22017MR291174
  3. [3] N. Bourbaki - Groupes et algèbres de Lie, chap. 7-8, Paris, 1975. Zbl0483.22001
  4. [4] M. Hochster and J.L. Roberts - Rings of invariants of reductive groups acting on regular rings are Cohen - Macaulay, Adv. in Math., 13, 1974, 115-175. Zbl0289.14010MR347810
  5. [5] V.G. Kac, V.L. Popov et E.B. Vinberg - Sur les groupes linéaires algébriques dont l'algèbre des invariants est libre, C.R. Acad. Sci. Paris, 283, 1976, 875-878. Zbl0343.20023MR419468
  6. [6] V.G. Kac - Root systems, representations of quivers and invariant theory, Lecture Notes in Math., 996, 1982. Zbl0534.14004MR718127
  7. [7] D. Luna - Slices étales, Mém. Soc. Math. France, 33, p. 81-105. Zbl0286.14014MR342523
  8. [8] D. Luna - Adhérences d'orbites et invariants, Invent. Math., 29, 1975, 231-238. Zbl0315.14018MR376704
  9. [9] V.L. Popov - A finiteness theorem for representations with a free algebra of invariants, Izv. Akad. Nauk SSSR, 46, 1982, 347-370. Zbl0547.20034MR651651
  10. [10] V.L. Popov - Syzygies in the theory of invariants, Izv. Akad. Nauk SSSR, 47, 1983, 544-622. Zbl0573.14003MR703596
  11. [11] V.L. Popov - Stability criteria for the action of a semisimple group on a factorial manifold, Izv. Akad. Nauk SSSR, 34, 1970, 523-531. Zbl0261.14011MR262416
  12. [12] G.W. Schwarz - Représentations of simple Lie groups with regular ring of invariants, Invent. Math., 49, 1978, 167-191. Zbl0391.20032MR511189
  13. [13] R.P. Stanley - Combinatorial reciprocity theorems, Adv. in Math., 14, 1974, 194-253. Zbl0294.05006MR411982
  14. [14] R.P. Stanley - Combinatories and invariant theory, Proc. Sympos. Pure Math., 34, 1979, 345-355. Zbl0411.22006MR525334
  15. [15] E.B. Vinberg and A.L. Onishchik - Seminar on algebraic groups and Lie groups, Izdat. Moskov. Gos. Univ., Moscow, 1969. 

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