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

Abstract

Let G be a compact, connected Lie group, and let Hom(Zm,G) denote the space of commuting m-tuples in G. Baird proved that the cohomology of Hom(Zm,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(Z2,G) for simple, simply connected Lie groups G of rank 2.