Schubert calculus in Lie groups

TL;DR

This paper develops a unified method to compute the integral cohomology rings of all compact, simply connected Lie groups by combining Schubert calculus with spectral sequence techniques.

Contribution

It introduces a novel approach that combines Schubert calculus and spectral sequences to determine the cohomology rings of Lie groups uniformly.

Findings

Explicit descriptions of cohomology rings for various Lie groups

A new unified computational framework for Lie group cohomology

Insights into the topological structure of compact Lie groups

Abstract

Let $G$ be a Lie group with a maximal torus $T$. Combining Schubert calculus in the flag manifold $G/T$ with the Serre spectral sequence of the fibration $G\rightarrow G/T$, we construct the integral cohomology ring $H^{\ast}(G)$ uniformly for all compact and simply connected Lie groups $G$.