HIGHER DEFORMATIONS OF LIE ALGEBRA REPRESENTATIONS II

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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.
Original languageEnglish
Pages (from-to)232-255
Number of pages24
JournalNagoya Mathematical Journal
Volume244
Early online date2 Jun 2020
DOIs
Publication statusPublished - 25 Dec 2021

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