Schur functions and the invariant polynomials characterizing U(n) tensor operators

15Citations
Citations of this article
1Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We give a direct formulation of the invariant polynomialsμGq(n)(, Δi,;, xi,i + 1,) characterizing U(n) tensor operators 〈p, q, ..., q, 0, ..., 0〉 in terms of the symmetric functions Sλknown as Schur functions. To this end, we show after the change of variables Δi= γi- δiand xi, i + 1= δi- δi + 1thatμGq(n)(,Δi;, xi, i + 1,) becomes an integral linear combination of products of Schur functions Sα(, γi,) · Sβ(, δi,) in the variables {γ1,..., γn} and {δ1,..., δn}, respectively. That is, we give a direct proof thatμGq(n)(,Δi,;, xi, i + 1,) is a bisymmetric polynomial with integer coefficients in the variables {γ1,..., γn} and {δ1,..., δn}. By making further use of basic properties of Schur functions such as the Littlewood-Richardson rule, we prove several remarkable new symmetries for the yet more general bisymmetric polynomialsμmGq(n)(γ1,..., γn; δ1,..., δm). These new symmetries enable us to give an explicit formula for bothμmG1(n)(γ; δ) and1G2(n)(γ; δ). In addition, we describe both algebraic and numerical integration methods for deriving general polynomial formulas forμmGq(n)(γ; δ). © 1983.

Cite

CITATION STYLE

APA

Gustafson, R. A., & Milne, S. C. (1983). Schur functions and the invariant polynomials characterizing U(n) tensor operators. Advances in Applied Mathematics, 4(4), 422–478. https://doi.org/10.1016/0196-8858(83)90018-0

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free