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Contemporary Mathematics Symmetric Polynomials and HD-Quantum Vertex Algebras
 

Summary: Contemporary Mathematics
Symmetric Polynomials and HD-Quantum 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., Hall-Littlewood 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

  

Source: Anguelova, Iana - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics