Polynomially and infinitesimally injective modules

Stephen Donkin; Haralampos Geranios

doi:10.1016/j.jalgebra.2013.05.033

Polynomially and infinitesimally injective modules

Stephen Donkin, Haralampos Geranios

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	125 - 141
Number of pages	17
Journal	Journal of Algebra
Volume	392
Issue number	n/a
DOIs	https://doi.org/10.1016/j.jalgebra.2013.05.033
Publication status	Published - 15 Oct 2013

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10.1016/j.jalgebra.2013.05.033

http://www.sciencedirect.com/science/article/pii/S002186931300358X

Cite this

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title = "Polynomially and infinitesimally injective modules",

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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AB - 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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