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arXiv · 1704.02405

Polynomially and Infinitesimally Injective Modules

Stephen Donkin·Haralampos Geranios
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Abstract

The injective polynomial modules for a general linear group $G$ of degree $n$ are labelled by the partitions with at most $n$ parts. Working over an algebraically closed field of characteristic $p$, we consider the question of which partitions correspond to polynomially injective modules that are also injective as modules for the restricted enveloping algebra of the Lie algebra of $G$. The question is related to the "index of divisibility" of a polynomial module in general, and an explicit answer is given for $n=2$.

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Stephen Donkin, Haralampos Geranios. 2017-04-08. Polynomially and Infinitesimally Injective Modules. https://arxiv.org/abs/1704.02405

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