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

الأصل · EN

We introduce certain correlation functions (graded q--traces) associated to vertex operator algebras and superalgebras which we refer to as n--point functions. These naturally arise in the studies of representations of Lie algebras of differential operators on the circle Le1--Le2, M. We investigate their properties and consider the corresponding graded q--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 q--traces and the corresponding q--difference equations. In particular, our construction leads to correlation functions and q--difference equations investigated by S. Bloch and A. Okounkov BO.