The exceptional Lie algebra E7(−25): multiplets and invariant differential operators

Abstract

In the present paper, we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional algebra E7(−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 spacetime. 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.