Formal differential operators, vertex operator algebras and zeta--values , II
Abstract
We introduce certain correlation functions (graded --traces) associated to vertex operator algebras and superalgebras which we refer to as --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 --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 --traces and the corresponding --difference equations. In particular, our construction leads to correlation functions and --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