A rational theory for Clebsch-Gordan coefficients

Abstract

A theory of Clebsch-Gordan coefficients for $SL(2,C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory and properties of binomial coefficients. A computational algorithm is given based on Pascal's recurrence.

arXiv comment16 pages: Final version. Minor corrections. To appear in Contemporary Mathematics (Representation Theory and Harmonic Analysis on Symmetric Spaces)