= Opposite Weyl boost generators
{title2=$K_i^{(L)}=-i\sigma_i/2,\quad K_i^{(R)}=+i\sigma_i/2$}
With $K_i=M_{0i}$ and $M_{\mu\nu}=i\gamma_{\mu\nu}/2$ in the supplied mostly-minus index convention, the two <Weyl spinor> blocks have equal rotation generators $J_i=\sigma_i/2$ and opposite boost generators. A complex-linear intertwiner must commute with every <SU(2)> rotation and hence be scalar by the <Schur lemma>, but no nonzero scalar intertwines the opposite boosts. This proves inequivalence of the two complex representations; parity exchanges them.
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