Abstract
Techniques for obtaining generators of nonregular maximal subalgebras of Lie algebras, alternative to those of Dynkin, are developed. They exploit the use of orthogonal bases in weight space, which are related to quark weights. The projection from an algebra G to its nonregular subalgebras g is related to an orthogonal matrix. The roots of G which project onto roots of g can be simply specified in the orthogonal bases. The phases of the expansion coefficients of generators of g in terms of generators of G are specified in such a manner that, for a given G, the entire set { g} of maximal subalgebras have consistent phases. The condition e−β =e°β is satisfied for all generators of g. The generators of all maximal nonregular subalgebras of all exceptional algebras are exhibited.
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