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The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras

Available Formats:
Electronic ISBN: 978-1-4704-0111-5
Product Code: MEMO/111/532.E
116 pp
List Price: $41.00 MAA Member Price:$36.90
AMS Member Price: $24.60 Click above image for expanded view The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras Available Formats:  Electronic ISBN: 978-1-4704-0111-5 Product Code: MEMO/111/532.E 116 pp  List Price:$41.00 MAA Member Price: $36.90 AMS Member Price:$24.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1111994
MSC: Primary 17; 46; Secondary 22; 81;

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.

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

• 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
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Volume: 1111994
MSC: Primary 17; 46; Secondary 22; 81;

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.

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

• 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
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