The e^+e^-\rightarrow D_s^+D_{s1}(2536)^- and e^+e^-\rightarrow D_s^+D^*_{s2}(2573)^- processes are studied using data samples collected with the BESIII detector at center-of-mass energies from 4.530 to 4.946~GeV. The absolute branching fractions of D_{s1}(2536)^- \rightarrow \bar{D}^{*0}K^- and D_{s2}^*(2573)^- \rightarrow \bar{D}^0K^- are measured for the first time to be (35.9\pm 4.8\pm 3.5)\% and $(37.4\pm 3.1\pm... Show more