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HIGHER DEFORMATIONS OF LIE ALGEBRA REPRESENTATIONS II

Part of: Lie algebras and Lie superalgebras Linear algebraic groups and related topics

Published online by Cambridge University Press:  02 June 2020

MATTHEW WESTAWAY Open the ORCID record for MATTHEW WESTAWAY [Opens in a new window]
MATTHEW WESTAWAY*
Affiliation:
School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK email M.P.Westaway@bham.ac.uk
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Abstract

Steinberg’s tensor product theorem shows that for semisimple algebraic groups, the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the preceding paper in this series, deforming the distribution algebra of a higher Frobenius kernel yielded a family of deformations called higher reduced enveloping algebras. In this paper, we prove that the Steinberg decomposition can be similarly deformed, allowing us to reduce representation theoretic questions about these algebras to questions about reduced enveloping algebras. We use this to derive structural results about modules over these algebras. Separately, we also show that many of the results in the preceding paper hold without an assumption of reductivity.

MSC classification

Primary: 17B10: Representations, algebraic theory (weights)
Secondary: 17B35: Universal enveloping (super)algebras 17B50: Modular Lie (super)algebras 20G05: Representation theory
Type
Article
Information
Nagoya Mathematical Journal , Volume 244 , December 2021 , pp. 232 - 255
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Copyright
© 2020 Foundation Nagoya Mathematical Journal

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