On the vertices of indecomposable summands of certain Lefschetz modules
Group Theory
2011-09-28 v1 Representation Theory
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.
Keywords
Cite
@article{arxiv.1109.5761,
title = {On the vertices of indecomposable summands of certain Lefschetz modules},
author = {John Maginnis and Silvia Onofrei},
journal= {arXiv preprint arXiv:1109.5761},
year = {2011}
}
Comments
30 pages