Lie algebra and invariant tensor technology for g2

Abstract

Proceeding in analogy with su(n) work on lambda matrices and f- and d-tensors, this paper develops the technology of the Lie algebra g2, its seven dimensional defining representation gamma and the full set of invariant tensors that arise in relation thereto. A comprehensive listing of identities involving these tensors is given. This includes identities that depend on use of characteristic equations, especially for gamma, and a good body of results involving the quadratic, sextic and (the non-primitivity of) other Casimir operators of g2.