A generalization of Pillen’s theorem for principal series modules
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- by Yutaka Yoshii
- Proc. Amer. Math. Soc. 140 (2012), 3761-3768
- DOI: https://doi.org/10.1090/S0002-9939-2012-11395-4
- Published electronically: March 13, 2012
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Abstract:
Let $G$ be a connected, semisimple and simply connected algebraic group defined and split over the finite field of order $p$. Pillen proved in 1997 that the highest weight vectors of some Weyl $G$-modules generate the principal series modules as submodules for the corresponding finite Chevalley groups. This result is generalized in this paper.References
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Bibliographic Information
- Yutaka Yoshii
- Affiliation: Department of Liberal Studies, Nara National College of Technology, Yamatokoriyama, Nara, 639-1080, Japan
- MR Author ID: 867648
- Email: yyoshii@libe.nara-k.ac.jp
- Received by editor(s): April 29, 2011
- Published electronically: March 13, 2012
- Communicated by: Pham Huu Tiep
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 3761-3768
- MSC (2010): Primary 20C33
- DOI: https://doi.org/10.1090/S0002-9939-2012-11395-4
- MathSciNet review: 2944716