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arXiv · 1109.5761

On the vertices of indecomposable summands of certain Lefschetz modules

John Maginnis·Silvia Onofrei
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Abstract

We study the reduced Lefschetz module of the complex of p-radical and p-centric subgroups. We assume that the underlying group G has parabolic characteristic p and the centralizer of a certain noncentral p-element has a component with central quotient H a finite group of Lie type in characteristic p. A non-projective indecomposable summand of the associated Lefschetz module lies in a non-principal block of G and it is a Green correspondent of an inflated, extended Steinberg module for a Lie subgroup of H. The vertex of this summand is the defect group of the block in which it lies.

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John Maginnis, Silvia Onofrei. 2011-09-27. On the vertices of indecomposable summands of certain Lefschetz modules. https://arxiv.org/abs/1109.5761

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