EXPLICIT EQUATIONS FOR EXTERIOR SQUARE OF THE GENERAL LINEAR GROUP

摘要

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 w_2. Bibliography: 12 titles.