Explicit Equations for Exterior Square of the General Linear Group

Аннотация

Several explicit systems of equations defining the exterior square of the general linear group ⋀² GL_n as affine group scheme are presented. Algebraic ingredients of the equations, so called exterior numbers, are translated to the language of weight diagrams corresponding to a Lie group of type A_n−1 in the representation with the highest weight ϖ₂.