The Generalized Clebsch-Gordan Formula

Su(3) Clebsch-gordan Coefficients

The purpose of this paper is to find out a set of general recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and general group theoretical methods applied to SU(3). The following eight sections are devoted to a detailed treatment of the carrier spaces of the irreducible representations and their direct...

A Calculus for Su(3) Leading to an Algebraic Formula for the Clebsch-gordan Coefficients

ABSTRACT: We develop a simple computational tool for SU(3) analogous to Bargmann’s calculus for SU(2). Crucial new inputs are, (i) explicit representation of the Gelfand-Zetlin basis in terms of polynomials in four variables and positive or negative integral powers of a fifth variable (ii) an auxiliary Gaussian measure with respect to which the Gelfand-Zetlin states are orthogonal but not norma...

Representations of the Lie algebra ĝl ∞ and “ reciprocity formula ” for Clebsch – Gordan coefficients

A Clebsch-gordan Formula for Sl3(c) and Applications to Rationality

If R, S, T are irreducible SL3(C)-representations, we give an easy and explicit description of a basis of the space of equivariant maps R⊗S → T (Theorem 3.1). We apply this method to the rationality problem for invariant function fields. In particular, we prove the rationality of the moduli space of plane curves of degree 34. This uses a criterion which ensures the stable rationality of some qu...

2 00 1 Clebsch - Gordan coefficients and the binomial distribution

There appear to be two standard ways of calculation C-G coefficients in quantum mechanics. One method is to combine the “ladder” operator approach with orthogonality conditions. The second method is to use some type of closed form [2] which allows the coefficients to be calculated directly. However, the latter approach is at times considered “tedious” [2] and does not reveal any new information...