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Enright-Shelton Theory and Vogan’s Problem for Generalized Principal Series

Available Formats:
Electronic ISBN: 978-1-4704-0063-7
Product Code: MEMO/102/486.E
List Price: $38.00 MAA Member Price:$34.20
AMS Member Price: $22.80 Click above image for expanded view Enright-Shelton Theory and Vogan’s Problem for Generalized Principal Series Available Formats:  Electronic ISBN: 978-1-4704-0063-7 Product Code: MEMO/102/486.E  List Price:$38.00 MAA Member Price: $34.20 AMS Member Price:$22.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 1021993; 107 pp
MSC: 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 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

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1021993; 107 pp
MSC: 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 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.

• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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