Hilbert Ideals And Steenrod Operations In Modularvector Invariant Theory

Let GLn(Fq)be the general linear group of rank n over a finite field Fq and W be the standard representation of GLn(Fq).Let Un(Fq)denote the group of lower triangular matrices along with diagonals 1.In this thesis,we give a generating set for the Hilbert ideal of the invariant ring Fq[W ? W*]Un(Fq);we also find relations among these generators for n = 3 and 4.Further,we calculate the actions of the Steenrod operations on the generators of Fq[W ? W*]GLn(Fq).