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The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras
Hans Plesner Jakobsen
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Memoirs of the American Mathematical Society
1994; 116 pp; softcover
Volume: 111
ISBN-10: 0-8218-2593-3
ISBN-13: 978-0-8218-2593-8
List Price: US$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/111/532
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This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.

Readership

Researchers and Ph.D. students in mathematics and theoretical physics.

Table of Contents

  • Introduction
  • Classical Lie superalgebras
  • Background results
  • The unitarizable highest weight modules of \(A(n,m), m\neq n\)
  • Infinite dimensional unitary representations of \(A(n,m), m\neq n\)
  • \(A(n,n)\)
  • The unitarizable highest weight modules of \(B(m,n), m>0\)
  • The unitarizable highest weight modules of \(D(m,n)\)
  • Borderline cases
  • \(F(4)\)
  • \(G(3)\)
  • \(D(2,1,\alpha )\)
  • Further developments
  • Bibliography
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