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Hyperplane Arrangements, Springer Representations and Exponents

  • Abraham Broer
Part of the Progress in Mathematics book series (PM, volume 172)

Abstract

Let g be a complex semisimple Lie algebra with adjoint groupGandLa Levi subgroupLwith Lie algebra l. LetT < Lbe a maximal torus with Lie algebra t and W =N G T/Tthe Weyl group acting on t as a reflection group.

Keywords

Conjugacy Class Weyl Group Simple Root Parabolic Subgroup Maximal Torus 
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References

  1. [1]
    W.M. Beynon and N. SpaltensteinGreen functions of finite Cheval-ley groups oftypeE n(n = 6, 7, 8), J. Algebra88(1984), 584–614.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    W. Borho and H. KraftOber Bahnen und deren Deformationen bei linearen Aktionen reduktiver GruppenComment. Math. Heiv.54(1979), 61–104.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    A. BroerThe sum of generalized exponents and Chevalley’s restriction theorem for modules of covariantsIndag. Math., N.S.6(1995), 385–396.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    A. BroerNormal nilpotent varieties in F4J. Algebra207(1998), 427–448.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    A. BroerDecomposition varieties in semisimple Lie algebrasto appear in Can. J. Math.Google Scholar
  6. [6]
    A. BroerLectures on decomposition classesto appear in Broer (Ed.)Representation theories and algebraic geometryNATO ASI Series C, vol. 514, 39–83, Kluwer Academic Publishers, Dordrecht, 1998.Google Scholar
  7. [7]
    J.B. CarrellOrbits of the Weyl group and a theorem of De Concini and ProcesiComp. Math.60(1986), 45–52.MathSciNetMATHGoogle Scholar
  8. [8]
    C. De Concini and C. ProcesiSymmetric functions conjugacy classes and the flag varietyInvent. Math.64(1981), 203–219.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    W.H. HesselinkPolarizations in the classical groupsMath. Z.160(1978), 217–234.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    G.I. Lehrer and T. ShojiOn flag varieties hyperplane complements and Springer representations of Weyl groupsJ. Austral. Math. Soc. (Series A)49(1990), 449–485.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    P. Orlik and L. SolomonCoxeter arrangementsProc. Symp. Pure Math.40part 2 (1983), 269–291.MathSciNetGoogle Scholar
  12. [12]
    R.W. RichardsonConjugacy classes in parabolic subgroups of semisimple algebraic groupsBull. London Math. Soc.6(1974), 21–24.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    R.W. RichardsonDerivatives of invariant polynomials on a semi-simple Lie algebrainHarmonic analysis and operator theoryProc. Cent. Math. Anal Austr. Natl. Univ.15(1987), 228–241.Google Scholar
  14. [14]
    T. ShojiOn the Green polynomials ofaChevalley group of typeF4, Commun. in Algebra10(1982), 505–543.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    E. Sommers and P. TrapaThe adjoint representation in rings of functionsRepresentation Theory, Electronic J. of the Amer. Math. Soc.1(1997), 182–189.MathSciNetMATHGoogle Scholar
  16. [16]
    N. SpaltensteinClasses unipotentes et sous-groupes de BorelL.N.M. 946, Springer-Verlag, New-York, 1982.Google Scholar
  17. [17]
    N. SpaltensteinOn the reflection representation in Springer’s theoryComment. Math. Helvetici66(1991), 618–636.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Abraham Broer
    • 1
  1. 1.Département de mathématiques et de statistiqueUniversité de MontréalMontréal (Québec)Canada

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