2003/03/12 by Antun Milas, Milas, Antun
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #advanced mathematical theories #math.NT #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0303154
46 pages, LaTeX (10pt, small font), 1 figure, BibTex
arxiv created 2003/03/12 · openalex publication_date 2003/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeLe1--\citeLe2, \citeM. 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 \citeBO.