C O N T E N T S Chapter 1. Chapter 2. Chapter 3. Chapter 4. m / n Chapter 5. A{n,m), Chapter 6. Chapter 7. m 0 Chapter 8. Chapter 9. Chapter 10 . Chapter 11 . Chapter 12 Chapter 13 . References Introduction Classical Lie superalgebras Background results The unitarizable highest weight modules of A(n, m), Infinite dimensional unitary representations of m / n A(n,n) The unitarizable highest weight modules of B{m, n), The unitarizable highest weight modules of D(m, n) Borderline cases F(4) G(3) 2?(2,l,a) Further developments 1 4 11 19 29 43 45 64 78 87 102 106 112 115
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