Let V be a simple, rational, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5404_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-cofinite vertex operator algebra of CFT type, and let k be a positive integer. In this paper, we determine the fusion products of twisted modules for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5404_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$V^{\otimes k}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>V</mi> <mrow> <mo>⊗</mo> <mi>k</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5404_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$G = \left\langle g \right\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <mfenced close="〉" open="〈"> <mi>g</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> generated by any permutation <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5404_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$g \in S_{k}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>∈</mo> <msub> <mi>S</mi> <mi>k</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>.

Fusion Products of Twisted Modules in Permutation Orbifolds: II

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发表日期：

2025年8月6日

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Chongying Dong,
Feng Xu,
Nina Yu

摘要

Let V be a simple, rational, $C_{2}$ $C_{2}$ -cofinite vertex operator algebra of CFT type, and let k be a positive integer. In this paper, we determine the fusion products of twisted modules for $V^{\otimes k}$ $V^{\otimes k}$ and $G = \left\langle g \right\rangle $ $G = 〈g〉$ generated by any permutation $g \in S_{k}$ $g \in S_{k}$ .