This book investigates the composition series of generalized principal series representations induced from a maximal cuspidal parabolic subgroup of a real reductive Lie group. Boe and Collingwood study when such representations are multiplicity-free (Vogan's Problem #3) and the problem of describing their composition factors in closed form. The results obtained are strikingly similar to those of Enright and Shelton for highest weight modules. Connections with two different flag variety decompositions are discussed.

Readership

Advanced graduate students and researchers in the representation theory of Lie groups.

Table of Contents

• Notation and preliminaries
• Some \(Sp_n\mathbb R\) results
• Inducing from holomorphic discrete series
• The \(SO_e(2,N)\) cases
• The \(SU(p,q)\) case
• The exceptional cases
• Loewy length estimates
• Appendix: Exceptional data