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arXiv · 1501.00124

A modular invariance property of multivariable trace functions for regular vertex operator algebras

Matthew Krauel·Masahiko Miyamoto
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Abstract

We prove an $\text{SL}_2 (\mathbb{Z})$-invariance property of multivariable trace functions on modules for a regular VOA. Applying this result, we provide a proof of the inversion transformation formula for Siegel theta series. As another application, we show that if $V$ is a regular VOA containing a regular subVOA $U$ whose commutant $U^c$ is regular and satisfies $(U^c)^c =U$, then all simple $U$-modules appear in some simple $V$-module.

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Matthew Krauel, Masahiko Miyamoto. 2014-12-31. A modular invariance property of multivariable trace functions for regular vertex operator algebras. https://arxiv.org/abs/1501.00124

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