Boson realisation of the Lie algebra F4and non-trivial zeros of 6j symbols

Abstract

By decomposing the adjoint and lowest dimensional representations of the exceptional Lie algebra F4 in the reduction F4 to SO3, a boson realisation of a F4 generator basis is established on account of a standard tensor operator formalism. Such a basis clearly exhibits the non-trivial vanishing of two 6j coefficients (discarding Regge symmetries), a property which is closely related to the possible embedding of F4 into SO26. Prospects for the occurrence of more non-trivial zeros, related to exception groups of higher rank, are indicated.