Article ID Journal Published Year Pages File Type
4946017 Journal of Symbolic Computation 2017 16 Pages PDF
Abstract
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 presentation 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.
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