The Chow rings of the algebraic groups E_6, E_7, and E_8

TL;DR

This paper explicitly computes the Chow rings of the complex algebraic groups E_6, E_7, and E_8 using Schubert calculus, extending previous work on other algebraic groups.

Contribution

It provides the first explicit descriptions of the Chow rings for these exceptional groups, utilizing Schubert calculus techniques.

Findings

Explicit generators for the Chow rings are identified.

The method extends Schubert calculus to complex exceptional groups.

Results contribute to understanding algebraic cycles in these groups.

Abstract

We determine the Chow rings of the complex algebraic groups of the exceptional type E_6, E_7, and E_8, giving the explicit generators represented by the pull-back images of Schubert varieties of the corresponding flag varieties. This is a continuation of the work of R. Marlin on the computation of the Chow rings of SO_n, Spin_n, G_2, and F_4. Our method is based on Schubert calculus of the corresponding flag varieties, which has its own interest.