CONTENTS

4.2 Vertex operator representations of A,(1) (I 1), J9f(1) (I 1), £j(1) (I =

6, 7, 8) 66

4.3 Schur polynomials and 5(ZLZ) 70

4.4 An integral form for the vertex algebra VL 74

4.5 The embedding of the derived subalgebra t_ in a module for Vi,/ . . . 79

4.6 A family of irreducible integrable modules for t_ 84

4.7 A description for the unequal root length affine Lie algebras 91