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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rationality of $ G/P$ for a nonreduced parabolic subgroup-scheme $ P$


Author: Christian Wenzel
Journal: Proc. Amer. Math. Soc. 117 (1993), 899-904
MSC: Primary 14M17; Secondary 14M20, 20G15
MathSciNet review: 1123669
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Abstract: Let $ G$ be a semisimple linear algebraic group over an algebraically closed field $ K$ of characteristic $ p > 3$. We have described and classified all parabolic subgroup-schemes of $ G$ (Trans. Amer. Math. Soc. (to appear)). Here we will show that $ G/P$ is a rational projective variety also for a nonreduced parabolic subgroup-scheme $ P$ of $ G$.


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

  • [SL] Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335 (57 #6215)
  • [Sp] T. A. Springer, Linear algebraic groups, Birkhäuser, Boston, Basel, and Stuttgart, 1981.
  • [W] C. Wenzel, Classification of all parabolic subgroup schemes of a semi-simple linear algebraic group over an algebraically closed field, Trans. Amer. Math. Soc. (to appear).
  • [J] Jens Carsten Jantzen, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press, Inc., Boston, MA, 1987. MR 899071 (89c:20001)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1123669-1
PII: S 0002-9939(1993)1123669-1
Article copyright: © Copyright 1993 American Mathematical Society