Hilbert series for equivariant mappings restricted to invariant hyperplanes

• Tipo: Artigo em Revista Científica Internacional
• Data: 2000

Autores

stewart, i (Autor) Outra; dias, aps (Autor) FCUP

Revista

Título: Journal of Pure and Applied Algebra

Vol. 151

Páginas: 89-106

ISSN: 0022-4049

Editora: Elsevier

Indexação

ISI Web of Knowledge - 3 Citações

Scopus - 4 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 18