Basic Properties of the Exceptional Lie Groups

Abstract

The exceptional Lie groups playa significant role in elementary particle models involving octonionic coloured quark fields. Simple methods for calculating the basic properties of these groups are outlined here. Among the properties computed are the dimensions and Dynkin index eigenvalues of irreps and branching rules for the most important group-subgroup structures. Kronecker products and symmetrized Kronecker powers of irreps of the exceptional groups are resolved. The concepts of elementary multiplets and Schur functions (S-functions) are used to greatly simplify the calculations, making possible manual calculations that are well beyond the capabilities of modem computer algorithms based on the enumeration of weights.