Journal of the
Korean Mathematical Society JKMS

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod $p$ cohomology of a space, particularly for dihedral groups.

Keywords: invariant theory, unstable algebra, pseudoreflection group, Lie group, $p$-compact group, classifying space

MSC numbers: Primary 55R35; Secondary 13A50, 55P60