2-dimensional vector invariants of parabolic subgroups of \(Gl_ 2({\mathbb{F}}_ p)\) over the field \({\mathbb{F}}_ p^ 1\)
The paper studies the polynomial invariants of the general linear group \(Gl_2(\mathbb{F}_p)\), the special linear group \(Sl_2(\mathbb{F}_p)\), and the upper triangular group \(U_2(\mathbb{F}_p)\) acting as usual on two copies of a 2-dimensional vector space over the finite prime field \(\mathbb{F}_p\). The authors point out that these algebras of invariants are Cohen-Macaulay, and compute for each a free module basis over a suitably chosen homogeneous system of parameters.
polynomial invariants of the general linear group
scientific article; zbMATH DE number 932633
scientific article