×

zbMATH — the first resource for mathematics

Picard-Lefschetz theory for the coadjoint quotient of a semisimple Lie algebra. (English) Zbl 0861.22008
This paper was jointly reviewed with the author’s article [ibid. 121, No. 3, 579-611 (1995; Zbl 0851.22013)].

MSC:
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
PDF BibTeX Cite
Full Text: DOI EuDML
References:
[1] V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko: Singularities of Differentiable Maps, Volume II. Birkhäuser, Boston-Basel-Berlin, 1988
[2] D. Barbasch, D. Vogan: Primitive ideals and orbital integrals in complex classical groups. Math. Ann.259, 153–199 (1982) · Zbl 0489.22010
[3] A. Borel, J.C. Moore: Homology theory for locally compact spaces. Michigan Math. J.7, 137–159 (1960) · Zbl 0116.40301
[4] E. Brieskorn: Über die Auflösung gewisser Singularitäten von holomorphen Addildungen. Math. Ann.166, 76–102 (1966) · Zbl 0145.09402
[5] E. Brieskorn: Die Monodromie der isolierten Singularitäten von Hyperflächen. Manus. Math.2, 103–161 (1970) · Zbl 0186.26101
[6] D. Collingwood, W. McGovern: Nilpotent Orbits in Semisimple Lie Algebras. Van Nostrand Reinhold, New York, 1993 · Zbl 0972.17008
[7] C. De Concini, G. Lusztig, C. Procesi: Homology of the zero-set of a nilpotent vector field on a flag manifold. J. Amer. Math. Soc.1, 15–34 (1988) · Zbl 0646.14034
[8] P. Deligne, N. Katz: Sèminaire de Géometrie Algébrique du Bois-Marie 1967–1969. SGA7II. Lecture Notes in Math.340, Springer, 1970
[9] R. Hotta: On Joseph’s construction of Weyl group representations. Tôhoku Math. J.36, 49–74 (1984) · Zbl 0545.20029
[10] R. Hotta, T.A. Springer: A specialization theorem form certain Weyl group representations and an application to Green polynomials. Invent math.41, 113–127 (1977) · Zbl 0389.20037
[11] M. Kashiwara, P. Shapira. Sheaves on manifolds. Springer, New York, 1990
[12] B. Kostant, S. Rallis: Orbits and representations associated with symmetric spaces. Am. J. Math.93, 753–809 (1971) · Zbl 0224.22013
[13] T.Y. Lam: Young diagrams, Schur functions, the Gale-Ryser theorem, and a conjecture of Snapper. J. Pure Appl. Algebra10, 81–94 (1977) · Zbl 0373.05009
[14] S. Lefschetz: L’Analyse Situs et la Géometrie Algébrique. Gauthier-Villars. Paris, 1924. Reprinted in Selected Papers, Chelsea, New York, 1971
[15] S. Lefschetz: Topology, Amer. Math. Soc. Colloquium Publications, New York, 1930. Reprinted by Chelsea, New York, 1965
[16] T. Matsuki: The orbits on affine symmetric spaces under the action of minimal parabolic subgroups. J. Math. Soc. Japan31, 331–357 (1979) · Zbl 0396.53025
[17] J. Milnor: Singular Points of Complex Hypersurfaces. Annals of Math. Studies 61, Princeton U. Press, Princeton, 1968 · Zbl 0184.48405
[18] I. Mirković, T. Uzawa, K. Vilonen: Matsuki correspondence for sheaves. Invent. math.109, 231–245 (1992) · Zbl 0789.53033
[19] F. Pham: Singularités des systèmes différentiels de Gauss-Manin. Progress in Mathematics, Birkhäuser, Boston-Basel-Stuttgart, 1979
[20] É. Picard, G. Simart: Théorie des Fonctions Algébriques de Deux Variables Indépendantes. Gauthier-Villars, Paris 1897
[21] R.W. Richardson, T.A. Springer: The Bruhat order on symmetric varieties. Preprint, University of Utrecht, 1989 · Zbl 0704.20039
[22] R.W. Richardson, T.A. Springer: Combinatorics and geometry ofK-orbits on the flag manifold. Preprint, Australian National University, 1992 · Zbl 0840.20039
[23] W. Rossmann: The structure of semisimple symmetric spaces. Can. J. Math.31, 157–180 (1979) · Zbl 0393.53032
[24] W. Rossmann: Characters as contour integrals. In Lie Group Representations III, R. Herb et al., editors, Lecture Notes in Math.1077, Springer, 1984 375–388 · Zbl 0545.22017
[25] W. Rossmann: Nilpotent orbital integrals in a real semisimple Lie algebra and representations of Weyl groups. In Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Actes du colloque en l’honneur de Jacques Dixmier. A. Connes, et al., editors. Progess in Mathematics vol. 92, Birkhäuser 263–287 1990 · Zbl 0744.22012
[26] W. Rossmann: Invariant eigendistributions on a semisimple Lie algebra and homology classes on the conormal variety I: an integral formula; II: representations of Weyl groups. J. Funct.96, 130–154, 155–192 (1991) · Zbl 0755.22004
[27] J. Sekiguchi: Remarks on nilpotent orbits of a symmetric pair. J. Math. Soc. Japan39, 127–138 (1987) · Zbl 0627.22008
[28] P. Slodowy: Four lectures on simple groups and singularities. Communications of the Math. Inst., Rijksuniversiteit Utrecht, v. 11, (1) 1980 · Zbl 0425.22020
[29] P. Slodowy: Simple Singularities and Simple Algebraic Groups. Lecture Notes in Mathematics815 (2), Springer, 1980 · Zbl 0441.14002
[30] N. Spaltenstein: Classes Unipotentes et Sous-groupes de Borel. Lecture Notes in Mathematics815, Springer, 1982 · Zbl 0486.20025
[31] T.A. Springer: Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Invent. math.36, 173–207 (1976) · Zbl 0374.20054
[32] T.A. Springer: A construction of representations of Weyl groups. Invent. math.44, 279–293 (1978) · Zbl 0376.17002
[33] T.A. Springer: A generalization of the orthogonality relations of Green functions. Preprint (1993)
[34] R. Steinberg: On the desingularization of the unipotent variety. Invent. math.36, 209–312 (1976) · Zbl 0352.20035
[35] R. Thom: Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc.75, 240–284 (1969) · Zbl 0197.20502
[36] N. Wallach: Real Reductive Groups I. Academic Press, Inc., New York, 1988 · Zbl 0666.22002
[37] J. Wolf: The action of a real semisimple Lie group on a complex flag manifold 7. Bulletin A.M.S.75, 1121–1237 (1969) · Zbl 0183.50901
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.