Memoirs of the American Mathematical Society 1994; 116 pp; softcover Volume: 111 ISBN10: 0821825933 ISBN13: 9780821825938 List Price: US$41 Individual Members: US$24.60 Institutional Members: US$32.80 Order Code: MEMO/111/532
 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. 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
