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Unitary representations of maximal parabolic subgroups of the classical groups

About this Title

Joseph A. Wolf

Publication: Memoirs of the American Mathematical Society
Publication Year: 1976; Volume 8, Number 180
ISBNs: 978-0-8218-2180-0 (print); 978-1-4704-0827-5 (online)
DOI: https://doi.org/10.1090/memo/0180
MathSciNet review: 0444847

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Table of Contents

Chapters

  • 0. Introduction
  • Part I. Linear groups
  • 1. Parabolic subgroups of general linear groups
  • Part II. Unitary groups
  • 2. Parabolic subgroups of unitary groups: Statement of structure
  • 3. Parabolic subgroups of unitary groups: Proof of structure
  • 4. Unitary representations of the nilradical
  • 5. Representations of the groups $G_{s;t,u}(F)$
  • 6. Representations of the maximal parabolic subgroups
  • 7. Representations of the little-groups $J_{d;e,a,b}(F)$
  • Part III. Symplectic groups
  • 8. Parabolic subgroups of symplectic and metaplectic groups
  • 9. Representations of the nilradical and the intermediate group
  • 10. Representations of the maximal parabolic subgroups
  • 11. Representations of the little-groups $J_{d;u,2v}(F)$
  • Part IV. Orthogonal groups
  • 12. Parabolic subgroups of complex orthogonal groups
  • 13. Structure of parabolic subgroups of $\mathrm {SO}^*(2m)$
  • 14. The nilradical and the intermediate group for $\mathrm {SO}^*(2m)$
  • 15. Representations of the maximal parabolic subgroups of $\mathrm {SO}^*(2m)$
  • Appendix. Induced representation