Pacific Journal of Mathematics

Desingularizations of some unstable orbit closures.

Mark Reeder

Article information

Source
Pacific J. Math., Volume 167, Number 2 (1995), 327-343.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102620870

Mathematical Reviews number (MathSciNet)
MR1328333

Zentralblatt MATH identifier
0851.22007

Subjects
Primary: 22E46: Semisimple Lie groups and their representations

Citation

Reeder, Mark. Desingularizations of some unstable orbit closures. Pacific J. Math. 167 (1995), no. 2, 327--343. https://projecteuclid.org/euclid.pjm/1102620870


Export citation

References

  • [B] A. Borel, Linear Algebraic Groups, Springer-Verlag, 1991.
  • [Ca] R. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complexc Characters, Wiley, 1985.
  • [G-M] M. Goresky and R. MacPherson, Intersection homology II,Invent. Math., 72 (1983), 77-129.
  • [G] V. Ginsburg, Proof of Deligne-Langlands conjecture, Doklady, 35 (1987), 304-308.
  • [H] W. Hesselink, The normality of closures of orbits in a Lie algebra,Com- ment. Math. Helv., 54 (1979), 105-110.
  • [H2] W. Hesselink, Desingularizations of varieties of nullforms, Invent. Math., 55 (1979), 141-163.
  • [J] J. C. Janzten, Moduln mit Einem Hchsten Gewicht, vol. 750, Springer- Verlag.
  • [K-L] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math., 87 (1987), 153-215.
  • [K] G. Kempf, On the collapsing of homogeneous bundles, Invent. Math., 37 (1976), 229-239.
  • [Ko] B. Kostant, The principal three dimensional subgroup and the Betti num- bers of a complex simple Lie group, Amer. J. Math., 81 (1959), 973-1032.
  • [K-R] B. Kostant and S. Rallis, Orbits and representations associated with sym- metric spaces, Amer. J. Math., 93 (1971), 753-809.
  • [M] T. Matsuki, The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan, 31 (1979), 331-357.
  • [R] M. Reeder, Whittaker functions, prehomogeneous vector spaces and stan- dard representations of p-adic groups, J. reine angew. Math., (1994), 83-121.
  • [Ril] R. W. Richardson, Conjugacy classes in Lie algebras and algebraic groups, Ann. Math., 86 (1967), 1-15.
  • [Ri2] R. W. Richardson, Conjugacy classes in parabolic subgroups of semisimple algebraic
  • [Ri3] R. W. Richardson, On orbits of algebraic groups and Lie groups, Bull.Austral. Math. Soc, 25 (1982), 1-28.
  • [Ru] H. Rubenthaler, Espaces ectoriels prehomogenes, sous-groupes paraboliques et sl2-triplets, C.R. Acad. Sci. Paris, Ser. A, 209 (1980), 127-129.
  • [S-K] M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65 (1977), 1-155.
  • [Se] J. Sekiguchi, The nilpotent subvariety of the vector space associated to a symmetric pair, Publ. RIMS, Kyoto Univ., 20 (1984), 155-212.
  • [Sp] T. A. Springer, Some results on algebraic groups with involutions, Adv. Stud. Pure Math., vol. 6, Kinokuniya, North-Holland,1985, 525-543.
  • [S] R. Steinberg, Endomorphismsof algebraic groups, Mem. Amer. Math. Soc, 80 (1968).
  • [V] E. B. Vinberg, On the classification of nilpotent elements in graded Lie algebras,Doklady, 16 (1975), 1517-1520.
  • [Vo] D. Vogan, Associated Varieties and Unipotent Representations, Repre- sentations of reductive groups, Birkhauser 1991.
  • [Z2] A.V. Zelevinsky, A p-adic analogue of the Kazhdan-Lusztigconjecture, Funktsional. Anal, i Prilozhen., 15 (1981), 9-21.