Cabibbo-allowed charmed meson decays into a pseudoscalar meson and an axial-vector meson are studied. The charm to axial-vector meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise quark model. The dipole momentum dependence of the $D\to K$ transition form factor and the presence of a sizable long-distance $W$-exchange are the two key ingredients for understanding the data of $D\to \bar Ka_1$. The $K_{1A}-K_{1B}$ mixing angle of the strange axial-vector mesons is found to be $\approx \pm37^\circ$ or $\pm58^\circ$ from $��\to K_1��_��$ decays. The study of $D\to K_1(1270)��, K_1(1400)��$ decays excludes the positive mixing-angle solutions. It is pointed out that an observation of the decay $D^0\to K_1^-(1400)��^+$ at the level of $5\times 10^{-4}$ will rule out $��\approx -37^\circ$ and favor the solution $��\approx -58^\circ$. Though the decays $D^0\to \bar K_1^0��^0$ are color suppressed, they are comparable to and even larger than the color-allowed counterparts: $\bar K_1^0(1270)��^0\sim K_1^-(1270)��^+$ and $\bar K_1^0(1400)��^0> K_1^-(1400)��^+$. The finite width effect of the axial-vector resonance is examined. It becomes important for $a_1(1260)$ in particular when its width is near 600 MeV.

19 pages