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Mathematics > Quantum Algebra

arXiv:1501.00124 (math)
[Submitted on 31 Dec 2014 (v1), last revised 26 Aug 2015 (this version, v2)]

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

Authors: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.
Comments: 18 pages, additional references added, typos corrected, and some additional information included
Subjects: Quantum Algebra (math.QA)
Cite as: arXiv:1501.00124 [math.QA]
  (or arXiv:1501.00124v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.1501.00124
Journal reference: J. Algebra. Volume 444, pp 124-142, (2015)

Submission history

From: Matthew Krauel [view email]
[v1] Wed, 31 Dec 2014 12:46:47 UTC (16 KB)
[v2] Wed, 26 Aug 2015 14:57:22 UTC (17 KB)
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