Electronic ISBN:  9781470401115 
Product Code:  MEMO/111/532.E 
116 pp 
List Price:  $41.00 
MAA Member Price:  $36.90 
AMS Member Price:  $24.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 111; 1994MSC: 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 antilinear antiinvolutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.
ReadershipResearchers and Ph.D. students in mathematics and theoretical physics.

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


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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 antilinear antiinvolutions, 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