Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

FCT[SFRH/BPD/34534/2006]

Fundação para a Ciência e a Tecnologia de Portugal (FCT)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

FAPESP[07/03519-6]

CNPq

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Portuguese and European Community structural funds

Fundação para a Ciência e a Tecnologia de Portugal (FCT)