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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Constructions for infinitesimal group schemes


Authors: Eric M. Friedlander and Julia Pevtsova
Journal: Trans. Amer. Math. Soc. 363 (2011), 6007-6061
MSC (2010): Primary 16G10, 20C20, 20G40
Published electronically: June 15, 2011
MathSciNet review: 2817418
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Abstract: Let $ G$ be an infinitesimal group scheme over a field $ k$ of characteristic $ p >0$. We introduce the global $ p$-nilpotent operator $ \Theta_G: k[G] \to k[V(G)]$, where $ V(G )$ is the scheme which represents 1-parameter subgroups of $ G$. This operator $ \Theta_G$ applied to $ M$ encodes the local Jordan type of $ M$ and leads to computational insights into the representation theory of $ G$. For certain $ kG$-modules $ M$ (including those of constant Jordan type), we employ $ \Theta_G$ to associate various algebraic vector bundles on $ \mathbb{P}(G)$, the projectivization of $ V(G)$. These vector bundles not only distinguish certain representations with the same local Jordan type, but also provide a method of constructing algebraic vector bundles on $ \mathbb{P}(G)$.


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Additional Information

Eric M. Friedlander
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Email: eric@math.northwestern.edu, ericmf@usc.edu

Julia Pevtsova
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Email: julia@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05330-4
PII: S 0002-9947(2011)05330-4
Received by editor(s): April 24, 2009
Received by editor(s) in revised form: February 9, 2010, and February 22, 2010
Published electronically: June 15, 2011
Additional Notes: The first author was partially supported by NSF grant #0300525
The second author was partially supported by NSF grant #0629156
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.