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Marques Ferreira, Jorge Nélio

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0000-0003-1364-5791

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2005 - 200912010 - 20173
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  • The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic
    Publication . Ferreira, Jorge N. M.; Fleischmann, Peter
    Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.
    2017Journal article Open access Show more
  • Funções teste e funções generalizadas em dimensão 1. Descrição e caracterização
    Publication . Ferreira, Jorge; Gouveia, Délia; Reis, Maurício; Silva, José Luís
    Neste trabalho introduzimos uma família de espaços de funções teste definidas em R associadas à medida Gaussiana µ. Por dualidade obtemos a correspondente família de espaços de distribuições (ou funções generaliza das). A caracterização destas famílias à custa de funções inteiras com um certo tipo de crescimento é feita usando a transformada S. Como exemplo de aplicação apresentamos o produto de Wick entre funções generalizadas.
    2005Journal article Open access Show more
  • The invariant fields of the Sylow groups of classical groups in the natural characteristic
    Publication . Ferreira, Jorge N. M.; Fleischmann, Peter
    Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.
    2016Journal article Open access Show more
  • On invariant Rings of Sylow subgroups of finite classical groups
    Publication . Ferreira, Jorge Nélio Marques; Peter Fleischmann
    In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.
    2011Doctoral thesis Open access Show more