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The full set of unitarizable highest weight modules of basic classical Lie superalgebras

About this Title

Hans Plesner Jakobsen

Publication: Memoirs of the American Mathematical Society
Publication Year: 1994; Volume 111, Number 532
ISBNs: 978-0-8218-2593-8 (print); 978-1-4704-0111-5 (online)
DOI: https://doi.org/10.1090/memo/0532
MathSciNet review: 1214730
MSC: Primary 17B10

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Classical Lie superalgebras
  • 3. Background results
  • 4. The unitarizable highest weight modules of $A(n, m)$, $m \neq n$
  • 5. Infinite dimensional unitary representations of $A(n, m)$, $m \neq n$
  • 6. $A(n, n)$
  • 7. The unitarizable highest weight modules of $B(m, n)$, $m > 0$
  • 8. The unitarizable highest weight modules of $D(m, n)$
  • 9. Borderline cases
  • 10. $F(4)$
  • 11. $G(3)$
  • 12. $D(2, 1, \alpha )$
  • 13. Further developments