Hilbert series for equivariant mappings restricted to invariant hyperplanes
UNSPECIFIED. (2000) Hilbert series for equivariant mappings restricted to invariant hyperplanes. JOURNAL OF PURE AND APPLIED ALGEBRA, 151 (1). pp. 89-106. ISSN 0022-4049Full text not available from this repository.
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. (C) 2000 Elsevier Science B.V. All rights reserved.
MSC: 13A50; 34A47; 58F14; 20C40.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||JOURNAL OF PURE AND APPLIED ALGEBRA|
|Publisher:||ELSEVIER SCIENCE BV|
|Official Date:||17 July 2000|
|Number of Pages:||18|
|Page Range:||pp. 89-106|
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