Lusztig's original character formula conjecture

Let $G_{\Bbbk}$ be a semisimple algebraic group with weight lattice $X$, positive roots $\Phi_+$, affine Weyl group $\Wa$, Coxeter number $h$, and $p$-dilated dot action $\pdot$. Let $\mu\in C_-^p$ be $p$-regular, let $x\in\Wa$ satisfy $x\pdot\mu\in X_+$, and write $L_{x\pdot\mu}$ and $\Delta_{y\pdot\mu}$ for the corresponding simple and standard modules. Let $\varepsilon_{yx}$ and $h_{y,x}(1)$ be the coefficients appearing in the affine Kazhdan–Lusztig character formula. Lusztig's character formula conjecture. If $p\ge h$ and

$$\langle\alpha^\vee,x\pdot\mu+\rho\rangle\le p(p-h+2)$$

for every $\alpha\in\Phi_+$, then

$$[ L_{x\pdot\mu} ] = \sum_{y\le x\atop y\pdot\mu\in X^+} \varepsilon_{yx}h_{y,x}(1)[\Delta_{y\pdot\mu}].$$

This is the original, conditional form of Lusztig's character formula, giving characters of simple modules in terms of standard modules under Jantzen's condition. Its resolution status is not specified in the supplied text.