On fusion rules and intertwining operators for the Weyl vertex algebra

07/08/2019 Rafael Mrđen Publikacije, Jedinica za teoriju reprezentacija Liejevih algebri, teoriju brojeva i pridružene strukture 0

Authors: Dražen Adamović, Veronika Pedić
Journal of Mathematical Physics 60, 081701 (2019);
https://doi.org/10.1063/1.5098128
Abstract: In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra. This way, we confirm the conjecture on fusion rules based on the Verlinde formula. We explicitly construct intertwining operators appearing in the formula for fusion rules. We present a result which relates irreducible weight modules for the Weyl vertex algebra to the irreducible modules for the affine Lie superalgebra  \hat{gl}(1|1).