English

Formal differential operators, vertex operator algebras and zeta--values , II

Quantum Algebra 2007-05-23 v1 Number Theory Representation Theory

Abstract

We introduce certain correlation functions (graded qq--traces) associated to vertex operator algebras and superalgebras which we refer to as nn--point functions. These naturally arise in the studies of representations of Lie algebras of differential operators on the circle \cite{Le1}--\cite{Le2}, \cite{M}. We investigate their properties and consider the corresponding graded qq--traces in parallel with the passage from genus 0 to genus 1 conformal field theory. By using the vertex operator algebra theory we analyze in detail correlation functions in some particular cases. We obtain elliptic transformation properties for qq--traces and the corresponding qq--difference equations. In particular, our construction leads to correlation functions and qq--difference equations investigated by S. Bloch and A. Okounkov \cite{BO}.

Keywords

Cite

@article{arxiv.math/0303154,
  title  = {Formal differential operators, vertex operator algebras and zeta--values , II},
  author = {Antun Milas},
  journal= {arXiv preprint arXiv:math/0303154},
  year   = {2007}
}

Comments

46 pages, LaTeX (10pt, small font), 1 figure, BibTex