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