Gröbner bases and invariant theory

AbstractIn this paper we study the relationship between Buchberger's Gröbner basis method and the straightening algorithm in the bracket algebra. These methods will be introduced in a self-contained overview on the relevant areas from computational algebraic geometry and invariant theory. We prove that a certain class of van der Waerden syzygies forms a Gröbner basis for the syzygy ideal in the bracket ring. We also give a description of a reduced Gröbner basis in terms of standard and non-standard tableaux. Some possible applications of straightening for symbolic computations in projective geometry are indicated