Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional algebra $E_{7(-25)}$. Our choice of this particular algebra is motivated by the fact that it belongs to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of $n$-dimensional Minkowski space-time. This class of algebras is identified and summarized in a table. Another motivation is related to the AdS/CFT correspondence. We give the multiplets of indecomposable elementary representations, including the necessary data for all relevant invariant differential operators.
Comment: 20 pages, 2 figures, TEX with input files harvmac.tex, amssym.def, amssym.tex; v2: added references; v3: change of normalization in f-lae (4.1) and (4.7); v4 corrected misprint. arXiv admin note: substantial text overlap with arXiv:0812.2655