Some New Applications of Weyl's Multipolarization Operators

Abstract

In Weyl's "The Classical Groups", he introduces some some remarkable differential operators, which he calls "quasi-compositions" of the polarization operators Dij. In the present paper, an equivalent combinatorial formulation is obtained for these operators, and is then used to obtain explicit formulas for the differentials in certain complexes (constucted by Zelevinsky, and further studied by Verma, Akin et al.) which furnish higher syzygies for the Pluecker equations, and also for the defining relations for Weyl modules.