Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras

摘要: In the present paper we continue project of systematic construction invariant differential operators for non-compact semisimple Lie groups. Our starting points is class algebras, which call 'conformal algebras' (CLA), have very similar properties to conformal algebras Minkowski space-time, though our aim go beyond this in a natural way. For introduce new notion {\it parabolic relation} between two g and g' that same complexification possess maximal subalgebras with complexification. Thus, consider exceptional algebra E_{7(7)} parabolically related CLA E_{7(-25)}, including E_{6(6)} E_{6(-6)} . Other interesting examples are orthogonal so(p,q) all so(n,2) p+q=n+2, Lorentz subalgebra so(n-1,1) its analogs so(p-1,q-1). We also E_{6(2)} hermitian symmetric case E_{6(-14)}, real forms sl(6). give formula number representations main multiplets valid CLAs them. considered cases indecomposable elementary necessary data relevant operators. reduced multiplets. should stress given most economic way pairs shadow fields}. Furthermore classification includes as special possible conservation laws} conserved currents}, unitary or not.