Heisenberg Parabolic Subgroup of SO^∗(10) 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 algebra so∗(10). We use the maximal Heisenberg parabolic subalgebra P=M⊕A⊕N with M=su(3,1)⊕su(2)≅so∗(6)⊕so(3). We give the main and the reduced multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERS. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebras so(p,q) (with p+q=10, p≥q≥2) with maximal Heisenberg parabolic subalgebra: P′=M′⊕A′⊕N′, M′=so(p−2,q−2)⊕sl(2,IR), M′C≅MC.

Keywords

• Heisenberg parabolic subgroup
• invariant differential operators
• SO^∗(10)