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

2003/03/12 by Antun Milas, Milas, Antun
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.NT #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0303152

52 pages, LaTeX (10pt, small font), BibTex

arxiv created 2003/03/12 · arxiv updated 2009/11/30

Abstract

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of ζ--functions at the negative integers. By using formal calculus techniques we discuss the appearance of values of ζ--functions at the negative integers underlying the construction. In addition we provide a conceptual explanation of this phenomena through several different notions of normal ordering via vertex operator algebra theory. We also derive a general Jacobi--type identity generalizing our previous construction. At the end we discuss related constructions associated to Dirichlet L--functions.

Related

• Vertex operator algebras and the zeta function
• Application of a "Jacobi identity" for vertex operator algebras to zeta values and differential operators
• Formal differential operators, vertex operator algebras and zeta--values , II
• Generalized Multiple q-Zeta Values and Characters of Vertex Algebras
• Vertex Operator Superalgebras and Odd Trace Functions