Using (10087±44)×10^{6} J/ψ events collected with the BESIII detector, numerous Ξ^{-} and Λ decay asymmetry parameters are simultaneously determined from the process J/ψ→Ξ^{-}Ξ[over ¯]^{+}→Λ(pπ^{-})π^{-}Λ[over ¯](n[over ¯]π^{0})π^{+} and its charge-conjugate channel. The precisions of α_{Λ0} for Λ→nπ^{0} and α[over ¯]_{Λ0} for Λ[over ¯]→n[over ¯]π^{0} compared to world averages are improved by factors of 4 and 1.7, respectively. The ratio of decay asymmetry parameters of Λ→nπ^{0} to that of Λ→pπ^{-}, ⟨α_{Λ0}⟩/⟨α_{Λ-}⟩, is determined to be 0.873±0.012_{-0.010}^{+0.011}, where the first and the second uncertainties are statistical and systematic, respectively. The ratio is smaller than unity more than 5σ, which signifies the existence of the ΔI=3/2 transition in Λ for the first time. Besides, we test for CP symmetry in Ξ^{-}→Λπ^{-} and in Λ→nπ^{0} with the best precision to date.