Let’s just do the version without the sum from the paper. So you want: $$\sum_{Y\in I} \chi(Y) c_{XY}^Z = \lambda \chi(Z)$$
Just take $\lambda = \chi(X)$.
Let’s just do the version without the sum from the paper. So you want: $$\sum_{Y\in I} \chi(Y) c_{XY}^Z = \lambda \chi(Z)$$
Just take $\lambda = \chi(X)$.