Explicit Fock representations of the classical Lie algebras in terms of boson creation and annihilation operators with an arbitrary highest weight are derived, and a general rule to construct Fock representations of a loop algebra from a boson realization of its corresponding Lie algebra is established. A new kind of lowest weight representations of the affine Lie algebras attached to the classical Lie algebras, which require a zero center, is also presented. Based on these, a simple affinization procedure is given to obtain the Fock representations of level 1 of these affijie Lie algebras.
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