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Nilpotent orbits, normality and Hamiltonian group actions
Author(s):
Ranee
Brylinski;
Bertram
Kostant
Journal:
J. Amer. Math. Soc.
7
(1994),
269-298.
MSC:
Primary 22E46;
Secondary 14L30, 22E60, 32M05, 58F06
MathSciNet review:
1239505
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References:
-
- [B]
- R. K. Brylinski, Twisted ideals of the nullcone, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (A. Connes et al., eds.), Birkhäuser, Boston, 1990, pp. 289-316. MR 1103594 (92e:17007)
- [B-K1]
- R. Brylinski and B. Kostant, The variety of all invariant symplectic structures on a homogeneous space and normalizers of isotropy groups, Symplectic Geometry and Mathematical Physics (P. Donato et al., eds.), Birkhäuser, Boston, 1991, pp. 80-113. MR 1156535 (94f:22008)
- [B-K2]
- -, Nilpotent orbits, normality and Hamiltonian group actions, Bull. Amer. Math. Soc. (N.S.) 26 (1992), 269-275. MR 1119160 (92k:22023)
- [C]
- R. W. Carter, Finite groups of Lie type: Conjugacy classes and complex characters, Wiley-Interscience, Chichester and New York, 1985. MR 794307 (87d:20060)
- [D]
- M. Demazure, Automorphismes et déformations des variétés de Borel, Invent. Math. 39 (1977), 179-186. MR 0435092 (55:8054)
- [Ge]
- S. Gelfand, The Weil representation of a Lie algebra of type
and related representations of , Funktsional. Anal. i Prilozhen. 14 (1980), no. 1, 51-52. (Russian) MR 565098 (81d:17003) - [Gr]
- W. A. Graham, Functions on the universal cover of the principal nilpotent orbit, Invent. Math 108 (1992), 15-27. MR 1156383 (93h:22026)
- [H]
- J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, Berlin and New York, 1972. MR 0323842 (48:2197)
- [K-S]
- J. Kimura and M. Sato, A classification of irreducible prehomogeneous spaces and their relative invariants, Nagoya Math. J. 65 (1977), 1-155. MR 0430336 (55:3341)
- [K1]
- B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex semisimple Lie group, Amer. J. Math. 81 (1959), 973-1032. MR 0114875 (22:5693)
- [K2]
- -, Lie group representations on polynomial rings, Amer J. Math. 85 (1963), 327-404. MR 0158024 (28:1252)
- [K3]
- -, Quantization and unitary representations, Lectures in Modern Analysis and Applications III, Lecture Notes in Math., vol. 170, Springer-Verlag, Berlin and New York, 1970, pp. 87-208. MR 0294568 (45:3638)
- [K4]
- -, The vanishing of scalar curvature and the minimal representation of
, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (A. Connes et al., eds.), Birkhäuser, Boston, 1990, pp. 85-124. MR 1103588 (92g:22031) - [Kr]
- H. Kraft, Closures of conjugacy classes in
, J. Algebra 126 (1989), 454-465. MR 1025000 (91a:17020) - [Kr-P]
- H. Kraft and C. Procesi, On the geometry of conjugacy classes in classical groups, Comment. Math. Helv. 57 (1982), 539-602. MR 694606 (85b:14065)
- [L-S]
- T. Levasseur and S. P. Smith, Primitive ideals and nilpotent orbits in type
, J. Algebra 114 (1988), 81-105. MR 931902 (89f:17013) - [McG]
- W. M. McGovern, Dixmier algebras and the orbit method, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (A. Connes et al., eds.), Birkhäuser, Boston, 1990, pp. 397-416. MR 1103597 (92f:17010)
- [M]
- D. Mumford, The red book of varieties and schemes, Lecture Notes in Math., vol. 1358, Springer-Verlag, Berlin and New York, 1988. MR 971985 (89k:14001)
- [So1]
- J.-M. Souriau, Structure des systémes dynamiques, Dunod, Paris, 1970. MR 0260238 (41:4866)
- [So2]
- -, Sur la variété de Kepler, Sympos. Math., vol. 14, Academic Press, London and New York, 1974, pp. 343-360. MR 0391646 (52:12466)
- [So3]
- -, Sur la variété de Kepler, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (Proc. IUTAM-ISIMM Modern Developments in Analytical Mechanics) 117(suppl.) (1983), 369-418.
- [S-S]
- T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups (A. Borel et al., eds.), Lecture Notes in Math., vol. 131, Springer-Verlag, New York, 1970, pp. 167-266. MR 0268192 (42:3091)
- [T]
- J. Tits, Espaces homogénes complexes compacts, Comment. Math. Helv. 37 (1962), 111-120. MR 0154299 (27:4248)
- [V-P]
- E. B. Vinberg and V. L. Popov, On a class of quasihomogeneous affine varieties, Math. USSR-Izv. 6 (1972), no. 4, 743-758.
- [V1]
- D. A. Vogan, The orbit method and primitive ideals for semisimple Lie algebras, Lie Algebras and Related Topics, CMS Conf. Proc., vol. 5, Amer. Math. Soc., Providence, RI, 1986, pp. 281-316. MR 832204 (87k:17015)
- [V2]
- -, Noncommutative algebras and unitary representations, Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, RI, 1988, pp. 35-60. MR 974331 (90a:22015)
- [Z]
- A. Zahid, Les endomorphismes
-finis des modules de Whittaker, Bull. Soc. Math. France 117 (1989), 451-477. MR 1042433 (91h:17010)
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Additional Information:
DOI:
10.1090/S0894-0347-1994-1239505-8
PII:
S0894-0347-1994-1239505-8
Copyright of article:
Copyright
1994,
American Mathematical Society
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