One-point restricted conformal blocks and the fusion tensor product

We investigate a one-point restriction of conformal blocks on (P¹,∞ ,1,0) ( P 1 , ∞ , 1 , 0 ) associated with modules over a vertex operator algebra V . By restricting the module attached to the point ∞ ∞ to its bottom degree, we obtain a new formula for computing fusion rules in terms of a new left A ( V )-module M¹ M² M 1 ⊙ M 2 over the Zhu algebra A ( V ), constructed from two V -modules M¹ M 1 and M² M 2 . As a consequence, for strongly rational vertex operator algebras, the construction of M¹ M² M 1 ⊙ M 2 induces the fusion tensor product on the module category Mod(A(V)) Mod ( A ( V ) ) .