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Invariant theory and reversible-equivariant vector fields |
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| Authors: | Fernando Antoneli Patrícia H Baptistelli Miriam Manoel |
| Institution: | a Centro de Matemática da Universidade do Porto (CMUP), Rua do Campo Alegre, 687, 4169-007 Porto, Portugal b Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo-Campus São Paulo, 05315-970 São Paulo SP, Brazil c Departamento de Matemática, Centro de Ciências Exatas, Universidade Estadual de Maringá, Av. Colombo, 5790, 87020-900 Maringá, PR, Brazil d Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal e Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil |
| Abstract: | 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-Poincaré 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. |
| Keywords: | 35B32 37G40 |
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