Abstract 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) ).
Jianqi Liu (Fri,) studied this question.