The integral cohomology ring of E_8/T

TL;DR

This paper provides a complete description of the integral cohomology ring of the flag manifold E_8/T, completing the classification for all compact connected simple Lie groups using Borel and Toda's method.

Contribution

It offers the first full computation of the integral cohomology ring for the E_8/T flag manifold, filling a gap in the understanding of Lie group topology.

Findings

Complete integral cohomology ring of E_8/T determined

Method extends to all compact simple Lie groups

Advances understanding of Lie group topology

Abstract

We give a complete description of the integral cohomology ring of the flag manifold E_8/T, where E_8 denotes the compact exceptional Lie group of rank 8 and T its maximal torus, by the method due to Borel and Toda. This completes the computation of the integral cohomology rings of the flag manifolds for all compact connected simple Lie groups.