On the GL(V)-module structure of K(n)^*(BV)

TL;DR

This paper investigates the module structure of Morava K-theory of classifying spaces of elementary abelian groups, using Brauer characters and computational methods to identify permutation modules.

Contribution

It introduces an algorithm to find maximal permutation submodules in modules over p-groups, advancing understanding of module structures in algebraic topology.

Findings

Morava K-theory modules are not always permutation modules

Developed an algorithm for identifying permutation submodules

Performed computational analysis using Brauer characters

Abstract

We study the question of whether the Morava K-theory of the classifying space of an elementary abelian group V is a permutation module (in either of two distinct senses) for the automorphism group of V. We use Brauer characters and computer calculations. We construct and implement an algorithm for finding permutation submodules of maximal dimension inside modules for p-groups in characteristic p.