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Enright-Shelton Theory and Vogan’s Problem for Generalized Principal Series
 
Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series
eBook 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
Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series
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Enright-Shelton Theory and Vogan’s Problem for Generalized Principal Series
eBook 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 publishers of book reviews
    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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.