A generalization of Weyl's identity for D_n

The expansion in Schur functions of the product Π_i<j (1-x_ix_j) is well known. It is more or less equivalent to Weyl's identity for root-systems of type D_n. In this paper we obtain the expansion in Schur functions of the product Π_i<j(1-∑_ℓ>0a_ℓ x_ix_j(x_i^ℓ-x_j ^ℓ)/(x_i-x_j)), thus generalizing Weyl's identity. We obtain this result by systematic calculation in fermionic Fock space. But familiarity with the latter is not a prerequisite for reading this paper. We develop from scratch the modest amount of theory that we need in elementary and purely algebraic fashion, taking pains to integrate the theory with classical symmetric function theory. The tools developed in this paper ought to have many further applications, e.g., to random matrix theory and to computational abelian function theory.