Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Classification of all parabolic subgroup-schemes of a reductive linear algebraic group over an algebraically closed field


Author: Christian Wenzel
Journal: Trans. Amer. Math. Soc. 337 (1993), 211-218
MSC: Primary 20G15; Secondary 11E57, 14L15, 14L17
DOI: https://doi.org/10.1090/S0002-9947-1993-1096262-1
MathSciNet review: 1096262
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a reductive linear algebraic group over an algebraically closed field $ K$. The classification of all parabolic subgroups of $ G$ has been known for many years. In that context subgroups of $ G$ have been understood as varieties, i.e. as reduced schemes. Also several nontrivial nonreduced subgroup schemes of $ G$ are known, but until now nobody knew how many there are and what there structure is. Here I give a classification of all parabolic subgroup schemes of $ G$ in $ \operatorname{char}(K) > 3$ .


References [Enhancements On Off] (What's this?)

  • [J] J. C. Jantzen, Algebraic groups and their representations, Academic Press, 1987. MR 899071 (89c:20001)
  • [H] W. Haboush, Central differential operators on split semi-simple groups over fields of positive characteristic, Proc. Séminaire d'Algèbre P. Dubreil et M.-P. Malliavin, 1979, Lecture Notes in Math., vol. 795, Springer, Berlin and New York, 1980, pp. 35-85. MR 582073 (82a:20049)
  • [P] V. L. Popov, Picard groups of homogeneous spaces of linear algebraic groups and onedimensional homogeneous vector bundles, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), no. 2; English transl., Math. USSR Izv. 8 (1974), no. 2. MR 0357399 (50:9867)
  • [SL] R. Steinberg, Lectures on Chevalley groups, Yale Univ., New Haven, Conn., 1968. MR 0466335 (57:6215)
  • [Sp] T. A. Springer, Linear algebraic groups, Birkhäuser, Boston, Mass., and Basel, 1981.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20G15, 11E57, 14L15, 14L17

Retrieve articles in all journals with MSC: 20G15, 11E57, 14L15, 14L17


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1096262-1
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society