MODULAR INVARIANT THEORY OF FINITE UNITARY GROUPS

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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

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