Equivariant Steinberg summands

We construct Steinberg summands of $G$-equivariant spectra with $\operatorname{GL}_n (\mathbb{F}_p)$-action. We prove a lemma about their fixed points when $G$ is a $p$-group, and then use this lemma to compute the fixed points of the Steinberg summand of the equivariant classifying space of $(\mathbb{Z} / p)^n$. These results will be used in a companion paper to study the layers in the $\operatorname{mod}$ $p$ symmetric power filtration for $H \underline{\mathbb{F}}_p$.

Keywords

equivariant, homology, homotopy

2010 Mathematics Subject Classification

20C20, 20G40, 55P42, 55P91

Full Text (PDF format)

Received 27 May 2019

Accepted 5 November 2019

Published 29 April 2020