 
Summary: Contemporary Mathematics
Symmetric Polynomials and HDQuantum Vertex Algebras
I. I. Anguelova
Abstract. In this paper we use a bicharacter construction to define an HD
quantum vertex algebra structure corresponding to the quantum vertex oper
ators describing classes of symmetric polynomials.
1. Introduction
Vertex operators were introduced in the earliest days of string theory and ax
ioms for vertex algebras were developed to incorporate these examples (see for
instance [FLM88]). Similarly, the definition of quantum vertex algebra should
be such that it accommodates the existing examples of quantum vertex operators
and their properties (see for instance [FJ88], [FR96], [BFJ98], [JM99] and many
others).
In this series of papers we study the quantum vertex algebra structure corre
sponding to classes of symmetric polynomials (e.g., HallLittlewood or Macdonald
polynomials). The vertex operators describing these polynomials were considered
by N. Jing in a series of papers ([Jin91], [Jin95], [Jin94b]). As shown for instance
by these examples a major difference between classical and quantum vertex alge
bras lies in the fact that two vertex operators (fields) Y (z) and Y (w) are no longer
`almost' commuting (i.e., commuting, except on the diagonal z = w), but instead
