  The transverse polarization of $\Lambda$ hyperon within reconstructed jets in
hadronic collisions offers a complementary platform to probe the polarized
fragmentation function $D_{1T}^\perp$. We illustrate that by performing a
global analysis of the transverse polarization of $\Lambda$ hyperons produced
in different kinematic regions and in different hadronic collisions, such as
$pp$, $p\bar p$, $pA$, and $\gamma A$ collisions, we can pin down the flavor
dependence of $D_{1T}^\perp$ which has been poorly constrained. Besides the
single inclusive jet production, the $\gamma/Z^0$-boson associated jet
production supplements with more capability in removing ambiguities in the
flavor dependence of $D_{1T}^\perp$.
