Cohomology of the spaces of commuting elements in Lie groups of rank two

Abstract

Let $G$ be the classical group, and let Hom$({\mathbb{Z}}^m,G)$ denote the space of commuting $m$-tuples in $G$. Baird proved that the cohomology of Hom$({\mathbb{Z}}^m,G)$ is identified with a certain ring of invariants of the Weyl group of $G$. In this paper by using the result of Baird we give the cohomology ring of Hom$({\mathbb{Z}}^2,G)$ for simple Lie group $G$ of rank 2.

7 pages