TY - JOUR
T1 - A generalization of Weyl's identity for Dn
AU - Anderson, Greg W.
PY - 2004/10
Y1 - 2004/10
N2 - The expansion in Schur functions of the product Πi (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(1-∑ℓ>0aℓ xixj(xiℓ-xj ℓ)/(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.
AB - The expansion in Schur functions of the product Πi (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(1-∑ℓ>0aℓ xixj(xiℓ-xj ℓ)/(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.
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U2 - 10.1016/j.aam.2004.01.001
DO - 10.1016/j.aam.2004.01.001
M3 - Article
AN - SCOPUS:4344712352
SN - 0196-8858
VL - 33
SP - 573
EP - 614
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
IS - 3
ER -