Bimodues associated to twisted modules of vertex operator algebras and fusion rules

2022/04/01 by Zhu, Yiyi
#17B69 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2204.00238

Abstract

Let V be a vertex operator algebra, T∈ ℕ and (M^k, Y_M^k) for k=1, 2, 3 be a g_k-twisted module, where g_k are commuting automorphisms of V such that g_k^T=1 for k=1, 2, 3 and g₃=g₁g₂. Suppose I(⋅, z) is an intertwining operator of type (arrayc M³ M¹ M² array) . We construct an A_g1g2(V)-A_g2(V)-bimodule A_{g1g2, g2}(M¹) which determines the action of M¹ from the bottom level of M² to the bottom level of M³ and explored its connections with fusion rules.

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