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The study of $\Lambda$ polarization in Semi-Inclusive Deep InelasticScattering (SIDIS) with a transversely polarized target has often beensuggested as a privileged way to access transversity, as the initial quarkpolarization can be transmitted to the hyperon and then observed via its weakdecay. COMPASS measured the $\Lambda$ transversity-induced polarization as afunction of Bjorken $x$, of the fraction $z$ of the longitudinal momentum ofthe fragmenting quark carried by the $\Lambda$ and of the $\Lambda$ transversemomentum $P_T$. The results are compatible with zero in all regions of phasespace. Under the hypothesis that transversity is a valence object, the previousknowledge of the transversity function allows to get information on the ratioof polarized and unpolarized $z-$integrated $\Lambda$ fragmentation functions.On the other hand, if the $\Lambda$ polarization is entirely due to the $s$quark, or if a quark-diquark model is applied, information can be obtained onthe $s$ quark transversity function.

Transversity and $\Lambda$ polarization at COMPASS