  Using $(10087\pm44)\times 10^{6}$ $J/\psi$ events collected with the BESIII
detector, numerous $\Xi^-$ and $\Lambda$ decay asymmetry parameters are
simultaneously determined from the process $J/\psi \to \Xi^- \bar{\Xi}^+ \to
\Lambda(p\pi^-) \pi^- \bar{\Lambda}(\bar{n} \pi^0) \pi^+$ and its
charge-conjugate channel. The precisions of $\alpha_0$ for $\Lambda \to n\pi^0$
and $\bar{\alpha}_0$ for $\bar{\Lambda} \to \bar{n}\pi^0$ compared to world
averages are improved by factors of 4 and 1.7, respectively. The ratio of decay
asymmetry parameters of $\Lambda \to n\pi^0$ to that of $\Lambda \to p\pi^-$,
$\langle \alpha_0 \rangle/ \langle \alpha_{\Lambda -} \rangle $, is determined
to be $ 0.873 \pm 0.012^{+0.011}_{-0.010}$, where the first and the second
uncertainties are statistical and systematic, respectively. The ratio is
smaller than unity more than $5\sigma$, which signifies the existence of the
$\Delta I = 3/2$ transition in $\Lambda$ for the first time. Beside, we test
for CP violation in $\Xi^- \to \Lambda \pi^-$ and in $\Lambda \to n \pi^{0}$
with the best precision to date.
