Hilbert series for equivariant mappings restricted to invariant hyperplanes

• Type: Article in International Scientific Journal
• Date: 2000

Authors

stewart, i (Author) Other; dias, aps (Author) FCUP

Journal

Title: Journal of Pure and Applied Algebra

Vol. 151

Pages: 89-106

ISSN: 0022-4049

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 4 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-ZGJ

DOI: 10.1016/s0022-4049(99)00021-3

Abstract (EN): In symmetric bifurcation theory it is often necessary to describe the restrictions of equivariant mappings to the fixed-point space of a subgroup. Such restrictions are equivariant under the normalizer of the subgroup, but this condition need not be the only constraint. We develop an approach to such questions in terms of Hilbert series - generating functions for the dimension of the space of equivariants of a given degree. We derive a formula for the Hilbert series of the restricted equivariants in the case when the subgroup is generated by a reflection, so the fixed-point space is a hyperplane. By comparing this Hilbert series with that of the normalizer, we can detect the occurrence of further constraints. The method is illustrated for the dihedral and symmetric groups.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18