Solvability, Structure, and Analysis for Minimal Parabolic Subgroups
- Author(s): Wolf, JA
- et al.
Published Web Locationhttps://doi.org/10.1007/s12220-017-9841-0
We examine the structure of the Levi component MA in a minimal parabolic subgroup P= MAN of a real reductive Lie group G and work out the cases where M is metabelian, equivalently where p is solvable. When G is a linear group we verify that p is solvable if and only if M is commutative. In the general case M is abelian modulo the center ZG , we indicate the exact structure of M and P, and we work out the precise Plancherel Theorem and Fourier Inversion Formulae. This lays the groundwork for comparing tempered representations of G with those induced from generic representations of P.