Vertex tensor category and Grothendieck fusion conjecture for $L_{-\frac{3}{2}}(\mathfrak{sl}_3)$

Let $\mathscr{D}$ be the category of weight $L_{-\frac{3}{2}}(\mathfrak{sl}_3)$-modules with finite-dimensional weight spaces and real weights. Let $\mathbin{\boxtimes}$ denote its tensor (fusion) product, and let the Grothendieck fusion rules be the rules referred to in equations (respect) and (grfusionrules). Vertex tensor category and Grothendieck fusion conjecture. The category $\mathscr{D}$ admits the structure of a vertex tensor category, and $\mathbin{\boxtimes}$ descends to the Grothendieck group with the stated Grothendieck fusion rules. The conjecture is used as a technical assumption for the subsequent parafermionic-coset analysis; the supplied text gives no resolution.