The $T$-equivariant integral cohomology ring of $F_4/T$

TL;DR

This paper computes the T-equivariant integral cohomology ring of the exceptional Lie group F4's flag manifold F4/T using combinatorial GKM theory, providing explicit algebraic descriptions.

Contribution

It offers a combinatorial determination of the T-equivariant integral cohomology ring of F4/T, a significant advancement in understanding the topology of exceptional Lie groups.

Findings

Explicit description of the cohomology ring structure.

Application of GKM theory to an exceptional Lie group.

Provides tools for further topological and geometric analysis.

Abstract

We determine the $T$-equivariant integral cohomology of $F_4/T$ combinatorially by the GKM theory, where T is a maximal torus of the exceptional Lie group $F_4$ and acts on $F_4/T$ by the left multiplication.