A generalization of Weyl's identity for Dn

Greg W. Anderson

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The expansion in Schur functions of the product Πi<j (1-xixj) is well known. It is more or less equivalent to Weyl's identity for root-systems of type Dn. In this paper we obtain the expansion in Schur functions of the product Πi<j(1-∑ℓ>0a xixj(xi-xj )/(xi-xj)), 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.

Original languageEnglish (US)
Pages (from-to)573-614
Number of pages42
JournalAdvances in Applied Mathematics
Issue number3
StatePublished - Oct 2004


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