The canonical-basis description of the principal-subspace ideal

Let $I_0$ be the ideal associated with the principal subspace $W_0$ in the completed quantum loop-algebra positive part, let $\mathcal{C}_0$ be the class of sheaves $\mathcal{F}\simeq\mathcal{O}(l_1)\oplus\cdots\oplus\mathcal{O}(l_n)$ with $l_1<l_2<\cdots<l_n<0$ and $l_{i+1}-l_i\geq2$, and define

$$\mathcal{P}_{W_0}=\{\mathbf{IC}(\mathcal{F})\mid\mathcal{F}\in\mathcal{C}_0\}.$$

Write $\mathbf{b}_{\mathbb{P}}$ for the canonical basis element indexed by $\mathbb{P}$. Principal-subspace ideal conjecture. One has

$$I_0=\widehat{\bigoplus}_{\mathbb{P}\notin\mathcal{P}_{W_0}}\mathbb{A}\mathbf{b}_{\mathbb{P}}.$$

This identifies the ideal through the canonical basis and would give a precise basis-theoretic description of the principal subspace quotient. The source presents it as conjectural; no resolution is supplied.