Functional Equations Satisfied by Intertwining Operators of Reductive Groups

This paper generalizes a recent work of Vogan and Wallach [VW] in which they derived a difference equation satisfied by intertwining operators of reductive groups. We show that, associated with each irreducible finitedimensional representation, there is a functional equation relating intertwining operators. In this way, we obtain natural relations between intertwining operators for different series of induced representations. 0. Introduction We use the convention of denoting a Lie group by a capital letter, and denoting its Lie algebra by the corresponding lower case German letter. A subscript C denotes complexification. Let G be a real reductive group, P = MAN a parabolic subgroup of G with a given Langlands decomposition [Kn], and c = c„ for a e Q>(P, A) and c„ some constant depending only on a, than the integral defining Received by the editors January 25, 1991. 1991 Mathematics Subject Classification. Primary 22E30, 22E46; Secondary 15A69.