UNSPECIFIED (2000) Hilbert series for equivariant mappings restricted to invariant hyperplanes. JOURNAL OF PURE AND APPLIED ALGEBRA, 151 (1). pp. 89-106. ISSN 0022-4049

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Abstract

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
ISSN:	0022-4049
Date:	17 July 2000
Volume:	151
Number:	1
Number of Pages:	18
Page Range:	pp. 89-106
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13178

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