Weyl group invariants

TL;DR

This paper proves that for most primes, the mod p cohomology of a Lie group's classifying space maps onto the Weyl group invariants of its maximal torus's classifying space, with a notable exception for E8 at p=3.

Contribution

It establishes the surjectivity of the homomorphism from the cohomology of Lie groups to Weyl invariants for all primes except one specific case.

Findings

The homomorphism is an epimorphism for all primes except p=3 when G=E8.

The result applies to compact simply-connected simple Lie groups.

Provides a comprehensive understanding of mod p cohomology invariants.

Abstract

For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants of the mod $p$ cohomology of the classifying space of its maximal torus is an epimorphism except for the case $p=3$, $G=E_8$.