Canonical construction of differential operators intertwining representations of real semisimple Lie groups (Q909043)

Let G be a real linear connected semisimple Lie group, \(P=MAN\) be a cuspidal parabolic subgroup of G. An induced representation \(T=Ind^ G_ P(\mu \otimes \nu \otimes 1)\) is called elementary representation of G (generalized principal series representation in another terminology). Here \(\mu\) is a discrete series representation of M, \(\nu\) is a character of A. T acts in some function space on G by left translations. In the present paper there are constructed differential operators which intertwine the elementary representations. These operators arise naturally from the right action of Lie G in functions on G. In detail the cases SL(2,\({\mathbb{R}})\) and \(SU^*(4)=Spin(5,1)\) are considered. There are some intersections with the earlier works by D. P. Zhelobenko and B. Kostant.