Support varieties for modules over Chevalley groups and classical Lie algebras
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- by Jon F. Carlson, Zongzhu Lin and Daniel K. Nakano PDF
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Abstract:
Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p>0$, $G_{1}$ be the first Frobenius kernel, and $G({\mathbb F}_{p})$ be the corresponding finite Chevalley group. Let $M$ be a rational $G$-module. In this paper we relate the support variety of $M$ over the first Frobenius kernel with the support variety of $M$ over the group algebra $kG({\mathbb F}_{p})$. This provides an answer to a question of Parshall. Applications of our new techniques are presented, which allow us to extend results of Alperin-Mason and Janiszczak-Jantzen, and to calculate the dimensions of support varieties for finite Chevalley groups.References
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Additional Information
- Jon F. Carlson
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 45415
- Email: jfc@math.uga.edu
- Zongzhu Lin
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- MR Author ID: 214053
- Email: zlin@math.ksu.edu
- Daniel K. Nakano
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 310155
- ORCID: 0000-0001-7984-0341
- Email: nakano@math.uga.edu
- Received by editor(s): April 21, 2005
- Received by editor(s) in revised form: October 17, 2005
- Published electronically: November 9, 2007
- Additional Notes: The research of the first author was supported in part by NSF grant DMS-0100662 and DMS-0401431
The research of the second author was supported in part by NSF grant DMS-0200673
The research of the third author was supported in part by NSF grant DMS-0102225 and DMS-0400548 - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 1879-1906
- MSC (2000): Primary 17B55, 20Gxx; Secondary 17B50
- DOI: https://doi.org/10.1090/S0002-9947-07-04175-X
- MathSciNet review: 2366967