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Categories of highest weight modules: applications to classical Hermitian symmetric pairs

About this Title

Thomas J. Enright and Brad Shelton

Publication: Memoirs of the American Mathematical Society
Publication Year: 1987; Volume 67, Number 367
ISBNs: 978-0-8218-2429-0 (print); 978-1-4704-0783-4 (online)
DOI: https://doi.org/10.1090/memo/0367
MathSciNet review: 888703
MSC: Primary 22E47; Secondary 17B10

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Table of Contents

Chapters

  • 1. Introduction and summary of results
  • Part I
  • 2. Notation
  • 3. Preliminary results
  • 4. Reduction of singularities
  • 5. The Zuckerman derived functors
  • 6. An equivalence of categories
  • 7. A second equivalence of categories
  • Part II. Highest weight modules for Hermitian symmetric pairs
  • 8. Statement of the main results
  • 9. Additional notation and preliminary results
  • 10. Wall shifting
  • 11. Induction from lower rank
  • 12. Proof of Theorem 8.4
  • 13. Proof of Theorem 8.5
  • 14. Projective resolutions and Ext
  • 15. Kazhdan-Lusztig polynomials
  • 16. Decompositions of $U(\underline {u}^-)$-free self-dual $\underline {g}$-modules