Algorithmic orbit classification for some Borel group actions

Hartmut Bürgstein; Wim H. Hesselink

Compositio Mathematica (1987)

  • Volume: 61, Issue: 1, page 3-41
  • ISSN: 0010-437X

How to cite


Bürgstein, Hartmut, and Hesselink, Wim H.. "Algorithmic orbit classification for some Borel group actions." Compositio Mathematica 61.1 (1987): 3-41. <>.

author = {Bürgstein, Hartmut, Hesselink, Wim H.},
journal = {Compositio Mathematica},
keywords = {nilpotent matrices; reductive algebraic group; Borel subgroup; algorithm; orbits},
language = {eng},
number = {1},
pages = {3-41},
publisher = {Martinus Nijhoff Publishers},
title = {Algorithmic orbit classification for some Borel group actions},
url = {},
volume = {61},
year = {1987},

AU - Bürgstein, Hartmut
AU - Hesselink, Wim H.
TI - Algorithmic orbit classification for some Borel group actions
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 61
IS - 1
SP - 3
EP - 41
LA - eng
KW - nilpotent matrices; reductive algebraic group; Borel subgroup; algorithm; orbits
UR -
ER -


  1. [1] A.V. Aho, J.E. Hopcroft, J.D. Ullman: Data structures and algorithms. Addison-Wesley: Reading (1983). Zbl0487.68005MR666695
  2. [2] A. Altman, S. Kleiman: Introduction to Grothendieck duality theory. Springer: Berlin etc. (1970). Zbl0215.37201MR274461
  3. [3] A. Borel: Linear algebraic groups. Benjamin: New York (1969). Zbl0186.33201MR251042
  4. [4] W. Borho: Über Schichten halfbeinfacher Lie-Algebren. Inventiones math.65 (1981) 283-317. Zbl0484.17004MR641132
  5. [5] W. Borho, P. Gabriel, R. Rentschler: Primideale in Einhüllenden auflösbarer Lie-Algebren. Springer: Berlin etc. (1973). Zbl0293.17005MR376790
  6. [6] E. Brieskorn: Singular elements of semisimple algebraic groups. Actes du Congrès International des Mathématiciens1970, tomeII p. 279-284. Zbl0223.22012MR437798
  7. [7] I.B. Brodskii: On orbits of unipotent groups. Funct. Ana. Appl.3 (1969) 96-100. Zbl0197.30405MR257268
  8. [8] A. Grothendieck: Torsion homologique et sections rationelles. Séminaire Anneaux de Chow et appl.2 (1958). 
  9. [9] A. Grothendieck, J.A. Dieudonné: Eléments de géométrie algébrique. Publ. Math. I.H.E.S.24 (1965). Zbl0135.39701
  10. [10] W.H. Hesselink: A classification of the nilpotent triangular matrices. Compositio Math.55 (1985) 89-133. Zbl0579.15011MR791648
  11. [11] D.A. Kazhdan, G. Lusztig: Representations of Coxeter groups and Hecke algebras. Inventiones math.53 (1979) 165-184. Zbl0499.20035MR560412
  12. [12] A.A. Kirillov: Elements of the theory of representations. Springer: Berlin etc. (1976). Zbl0342.22001MR412321
  13. [13] D. Mumford: Introduction to algebraic geometry (preliminary version of first 3 chapters) (1968). 
  14. [14] V. Pyasetskii: Linear Lie groups acting with finitely many orbits. Funct. Ana. Appl.9 (1975) 351-353. Zbl0326.22004
  15. [15] N. Spaltenstein: On the fixed point set of a unipotent element on the variety of Borel subgroups. Topology16 (1977) 203-204. Zbl0445.20021MR447423
  16. [16] N. Spaltenstein: Classes unipotentes et sous-groupes de Borel. Springer: Berlin etc. (1982). Zbl0486.20025MR672610
  17. [17] T.A. Springer: Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Inventiones math.36 (1976) 173-207. Zbl0374.20054MR442103
  18. [18] T.A. Springer: A construction of representations of Weyl groups. Inventiones math.44 (1978) 279-293. Zbl0376.17002MR491988
  19. [19] T.A. Springer: Linear algebraic groups. Birkhäuser: Boston etc. (1981). Zbl0453.14022
  20. [20] T.A. Springer, R. Steinberg: Conjugacy classes. Part E of: A. Borel et al.: Seminar on algebraic groups and related finite groups. Springer, Berlin etc. (1970). Zbl0249.20024MR268192

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