Twisted regular representations for vertex operator algebras
Twisted regular representations for vertex operator algebras
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DOI：
10.1016/j.jalgebra.2023.03.029
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发表时间：
2022-06
影响因子：
0.9
通讯作者：
Haisheng Li;Jiancai Sun
中科院分区：
文献类型：
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作者：
Haisheng Li;Jiancai Sun
本文主要研究顶点算子代数的扭曲正则表示。设V是一个顶点算子代数，σ1，σ2是V的交换有限序自同构，σ=(σ1σ2)−1.主要结果中，对任意σ扭曲V模W和任意非零复数z，我们构造了弱σ1⊗σ2扭曲V⊗V模Dσ1，σ2(Z)(W)在W⁎内.设W1，W2分别为σ1-扭V-模和σ2-扭V-模。证明了从W1⊗W2到W⁎的P(Z)-交织映射与弱σ1⊗σ2-扭转V⊗V模从W1⊗W2到Dσ1，σ2(Z)(W)的同态相同.我们还证明了从W1⊗W2到W⁎的P(Z)-交织映射等价于(W‘W1W2)型交织算子，这是Huang和Lepowsky的一个结果的一个扭曲版本.最后，我们证明了对每个τ-扭曲V-模M具有τV的任意有限阶自同构，q-分次迹函数的系数位于D-τ，τ−1(−-1)(V)中，并生成一个τ⊗τ−-1-扭曲V-⊗V-子模与M-⊗M‘同构.
This paper is to study what we call twisted regular representations for vertex operator algebras. Let V be a vertex operator algebra, let σ 1, σ 2 be commuting finite-order automorphisms of V and let σ=(σ 1 σ 2)− 1. Among the main results, for any σ-twisted V-module W and any nonzero complex number z, we construct a weak σ 1⊗ σ 2-twisted V⊗ V-module D σ 1, σ 2 (z)(W) inside W⁎. Let W 1, W 2 be σ 1-twisted, σ 2-twisted V-modules, respectively. We show that P (z)-intertwining maps from W 1⊗ W 2 to W⁎ are the same as homomorphisms of weak σ 1⊗ σ 2-twisted V⊗ V-modules from W 1⊗ W 2 into D σ 1, σ 2 (z)(W). We also show that a P (z)-intertwining map from W 1⊗ W 2 to W⁎ is equivalent to an intertwining operator of type (W′ W 1 W 2), which is a twisted version of a result of Huang and Lepowsky. Finally, we show that for each τ-twisted V-module M with τ any finite-order automorphism of V, the coefficients of the q-graded trace function lie in D τ, τ− 1 (− 1)(V) and generate a τ⊗ τ− 1-twisted V⊗ V-submodule isomorphic to M⊗ M′.