Classification of problematic subgroups of U(n)

TL;DR

This paper classifies certain p-toral subgroups of U(n) based on their fixed point properties in the complex of partitions, advancing understanding of subgroup actions on complex n-space.

Contribution

It provides a classification of problematic p-toral subgroups of U(n) with non-contractible fixed points, a novel insight into subgroup actions on partition complexes.

Findings

Identifies conditions for non-contractible fixed points.

Classifies problematic p-toral subgroups of U(n).

Enhances understanding of subgroup actions on complex spaces.

Abstract

We classify p-toral subgroups of U(n) that can have non-contractible fixed points under the action of U(n) on the complex of partitions of complex n-space into mutually orthogonal subspaces.