[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2010.47.2.299

INVARIANT RINGS AND DUAL REPRESENTATIONS OF DIHEDRAL GROUPS

Ishiguro, Kenshi (Department of Applied Mathematics, Fukuoka University)

Publication Information

Journal of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 299-309 More about this Journal

Abstract

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;

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