engleski

Bershadsky-Polyakov vertex algebras at positive integer levels and duality

We study the simple Bershadsky-Polyakov algebra W_k=W_k(sl_3, f_θ) at positive integer levels and classify their irreducible modules. In this way we confirm the conjecture from our previous paper. Next, we study the case k=1. We discover that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple affine vertex superalgebra L_k'(osp(1, 2)) for k'=-5/4. Using a free-field realization of L_k'(osp(1, 2)), we get a free-field realization of W_k and their highest weight modules. In a sequel, we plan to study fusion rules for W_k.

Vertex algebra ; W-algebras ; Bershadsky–Polyakov algebra ; Zhu’s algebra

nije evidentirano