Let $U_q(\hat{\mathfrak g})$ be a quantum affine algebra, and let $L$ be an integrable simple highest weight module of $U_q(\hat{\mathfrak g})$. In [Lu], Lusztig proved that the limit of $L$ when $q\to 1$ is the integrable simple highest weight module of the affine Kac-Moody Lie algebra $\hat{\mathfrak g}$. Does it hold true for non-integrable simple highest weight modules?
[Lu] G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. Math. 70 (1988), 237-249.
