Given a $\mathbb{C}$-linear braided fusion category $\mathcal{C}$ containing a fusion rule of the form e.g. \begin{equation}X\otimes Y\cong A\oplus B \oplus C\end{equation} (where $A,B, C, X$ and $Y$ are all simple objects with $A, B, C$ non-isomorphic), we can write the $R$-matrix $R^{XY}=\text{diag}(R^{XY}_{A}, R^{XY}_{B}, R^{XY}_{C})$. My intuition has always been that these scalars for two distinct objects cannot be the same (much like eigenvalues for distinct eigenspaces should not be the same). Is this misguided? That is,

**(Q)** Can we have scalars $R^{XY}_{A}=R^{XY}_{B}$ for $A\not\cong B$?

If $\mathcal{C}$ is *symmetric*, then I believe that diagonal matrix $R^{XY}$ can only have $\pm1$s along its diagonal. However, if the answer to **(Q)** is *no*, then this would mean that $\mathcal{C}$ can only contain fusion rules of the form $X\otimes Y\cong pA\oplus qB$ and $X\otimes Y\cong pA$ (where $p$ and $q$ are positive integers). This seems too strong.

Thanks!