Vertex Operators and Modular Forms
Tuite, Michael P.
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Geoffrey Mason and Michael P. Tuite(2009)Vertex Operators and Modular Forms, A Window into Zeta and Modular Physics, ed Kirsten, K. and Williams, F., MSRI Publications 57 (2010), 183--278 CUP
The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite group and its irreducible characters; the algebraic structure determines a set of numerical invariants, and arithmetic properties of the invariants provides feedback in the form of restrictions on the algebraic structure. One of the main points of these Notes is to explain how this works, and to give some reasonably interesting examples.