Einstein Manifold of SO(p, 9 – p), Its Corresponding Parabolic Subgroup, and Invariant Differential Operators

Abstract

In the present paper we continue the project of systematic explicit construction of invariant differential operators. On the example of the non-compact group SO(p,9 - p) (for p = 5,6) we give the classification multiplets of indecomposable elementary representations induced from suitable choice of parabolic subgroup MAN so that the factor-group {G mathord{left/ {vphantom {G M}} right. kern-0em} M} is an Einstein manifold. This classification includes the data for the relevant invariant differential operators.