A Z 2-orbifold model of the symplectic fermionic vertex by Abe T. PDF

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249 (2), 455–484 (2005) 2. : Rationality, regularity, and C2 -cofiniteness, Trans. Am. Math. Soc. 356 (8), 3391–3402 (2004) + 3. : Classification of irreducible modules for the vertex operator algebra VL ; general case. J. Algebra 273 (2), 657–685 (2004) 4. : A spanning set for VOA modules. J. Algebra 254, 125–151 (2002) 5. : Nonmeromorphic operator product expansion and C2 -cofiniteness for a family of W-algebras. J. Phys. A 39 (4), 951–966 (2006) 6. : Classification of irreducible modules for the vertex operator algebra M(1)+ .

Dong, Y. Arike and the referee for reading the manuscript and giving him some errors and comments. References + 1. : Rationality of the vertex operator algebra VL for a positive definite even lattice L. Math. Z. 249 (2), 455–484 (2005) 2. : Rationality, regularity, and C2 -cofiniteness, Trans. Am. Math. Soc. 356 (8), 3391–3402 (2004) + 3. : Classification of irreducible modules for the vertex operator algebra VL ; general case. J. Algebra 273 (2), 657–685 (2004) 4. : A spanning set for VOA modules.

5 The modular transformations of SSF ± (τ ) and SSF(θ )± (τ ) with respect to the transformations τ → τ + 1 and τ → − τ1 are given by SSF ± (τ + 1) = e SSF ± 1 − τ = 1 2d+1 dπi 6 SSF(θ )+ (τ ) − SSF(θ )− (τ ) ± SSF(θ )± (τ + 1) = ±e− SSF(θ )± − 1 τ = SSF ± (τ ), dπi 12 (−iτ )d (SSF + (τ ) − SSF − (τ )), 2 SSF(θ )± (τ ), 1 SSF(θ )+ (τ ) + SSF(θ )− (τ ) ± 2d−1 SSF + (τ ) + SSF − (τ ) . 2 Proof We see that φ1 (τ )2d = SSF(θ )+ (τ ) + SSF(θ )+ (τ ), φ2 (τ )2d = SSF(θ )+ (τ ) − SSF(θ )− (τ ) and φ3 (τ )2d = 2d SSF + (τ ) + SSF − (τ ) , η(τ )2d = SSF + (τ ) − SSF − (τ ).

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A Z 2-orbifold model of the symplectic fermionic vertex operator superalgebra by Abe T.


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