4次複素一般線型群の既約表現のテンソル積空間におけるグレブナー基底の特徴

Abstract

We will give the Zariski closure of the image of polynomial mappings from the set of all complex square matrices of order 𝑛 to a tensor product of irreducible representations of the complex general liner group of degree 𝑛. In this paper, we give the Zariski closure of the image of polynomial mappings from the set of all complex square matrices of order 4 to a tensor product of spaces of alternating 2-tensors on 4-dimensional complex vector spaces. We also describe features of the Gröbner basis of the ideal defining the Zariski closure.