Vertex operators and modular forms.

Geoffrey Mason; Michael P. Tuite

doi:10.13025/15344

Vertex operators and modular forms.

Geoffrey Mason
, Michael P. Tuite

Mathematics

Research output: Chapter in Book or Conference Publication/Proceeding › Conference Publication › peer-review

Abstract

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.

Original language	English (Ireland)
Title of host publication	A WINDOW INTO ZETA AND MODULAR PHYSICS, MATHEMATICAL SCIENCES RESEARCH INSTITUTE PUBLICATIONS , CAMBRIDGE UNIVERSITY PRESS, (CAMBRIDGE).
DOIs	https://doi.org/10.13025/15344
Publication status	Published - 1 Jan 2010

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10.13025/15344Licence: CC BY-NC-ND

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title = "Vertex operators and modular forms.",

abstract = "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.",

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N2 - 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.

AB - 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.

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ER -

Vertex operators and modular forms.

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