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A generalization of Pillen's theorem for principal series modules


Author: Yutaka Yoshii
Journal: Proc. Amer. Math. Soc. 140 (2012), 3761-3768
MSC (2010): Primary 20C33
DOI: https://doi.org/10.1090/S0002-9939-2012-11395-4
Published electronically: March 13, 2012
MathSciNet review: 2944716
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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.


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Additional Information

Yutaka Yoshii
Affiliation: Department of Liberal Studies, Nara National College of Technology, Yamatokoriyama, Nara, 639-1080, Japan
Email: yyoshii@libe.nara-k.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2012-11395-4
Received by editor(s): April 29, 2011
Published electronically: March 13, 2012
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2012 American Mathematical Society