  The representation theory of affine Kac-Moody Lie algebras has grown
tremendously since their independent introduction by Robert V. Moody and Victor
G. Kac in 1968. Inspired by mathematical structures found by theoretical
physicists, and by the desire to understand the ``monstrous moonshine'' of the
Monster group, the theory of vertex operator algebras (VOA's) was introduced by
Borcherds, Frenkel, Lepowsky and Meurman. An important subject in this young
field is the study of modules for VOA's and intertwining operators between
modules. Feingold, Frenkel and Ries defined a structure, called a vertex
operator para-algebra(VOPA), where a VOA, its modules and their intertwining
operators are unified. In this work, for each $l\geq 1$, we begin with the
bosonic construction (from a Weyl algebra) of four level $-\shf$ irreducible
representations of the symplectic affine Kac-Moody Lie algebra $C_l^{(1)}$. The
direct sum of two of these is given the structure of a VOA, and the direct sum
of the other two is given the structure of a twisted VOA-module. In order to
define intertwining operators so that the whole structure forms a VOPA, it is
necessary to separate the four irreducible modules, taking one As the VOA and
the others as modules for it. This work includes the bosonic analog of the
fermionic construction of a vertex operator superalgebra from the four level 1
irreducible modules of type $D_l^{(1)}$ given by Feingold, Frenkel and Ries.
While they only get a VOPA when $l = 4$ using classical triality, the
techniques in this work apply to any $l\geq 1$.
