Fusion in the W_3 algebra

TL;DR

This paper explores the fusion rules of the W_3 algebra's representations, extending existing theories and providing explicit calculations within a minimal model to deepen understanding of its structure.

Contribution

It introduces a new approach to fusion in the W_3 algebra and offers explicit calculations for a minimal model, advancing the theoretical framework.

Findings

Derived fusion rules for W_3 algebra representations

Provided explicit calculations for a specific minimal model

Enhanced understanding of W_3 algebra structure

Abstract

We develop the notions of fusion for representations of the W_3 algebra along the lines of Feigin and Fuchs. We present some explicit calculations for a W_3 minimal model.