Electronic ISBN:  9781470400637 
Product Code:  MEMO/102/486.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $22.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 102; 1993; 107 ppMSC: Primary 22;
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 multiplicityfree (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.
ReadershipAdvanced graduate students and researchers in the representation theory of Lie groups.

Table of Contents

Chapters

1. Introduction

2. Notation and preliminaries

3. Some $Sp_n\mathbb {R}$ results

4. Inducing from holomorphic discrete series

5. The $SO_e$(2, $N$) cases

6. The $SU$($p$, $q$) case

7. The exceptional cases

8. Loewy length estimates

9. Appendix. Exceptional data


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

Chapters

1. Introduction

2. Notation and preliminaries

3. Some $Sp_n\mathbb {R}$ results

4. Inducing from holomorphic discrete series

5. The $SO_e$(2, $N$) cases

6. The $SU$($p$, $q$) case

7. The exceptional cases

8. Loewy length estimates

9. Appendix. Exceptional data