Suspension splittings and self-maps of flag manifolds

TL;DR

This paper provides a new wedge decomposition of the suspension of flag manifolds G/T for compact Lie groups, using cohomological idempotents, and explores implications for self-maps of these spaces.

Contribution

It introduces a novel wedge decomposition of Sigma G/T by identifying cohomological idempotents, advancing understanding of the topology of flag manifolds.

Findings

Wedge decomposition of Sigma G/T established

Identification of cohomological idempotents in flag manifolds

New insights into self-maps of G/T spaces

Abstract

If $G$ is a compact connected Lie group and $T$ is a maximal torus, we give a wedge decomposition of $\Sigma G/T$ by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of $G/T$.