2023/10/24 by Chongying Dong, Dong, Chongying, Xingjun Lin +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2310.15563
For a rational and C2-cofinite vertex operator algebra V with an automorphism group G of prime order, the fusion rules for twisted V-modules are studied, a twisted Verlinde formula which relates fusion rules for g-twisted modules to the S-matrix in the orbifold theory is established. As an application of the twisted Verlinde formula, a twisted analogue of the Kac-Walton formula is proved, which gives fusion rules between twisted modules of affine vertex operator algebras in terms of Clebsch-Gordan coefficients associated to the corresponding finite dimensional simple Lie algebras.