= Conjugate fundamental spinor of SU(2)
{title2=$\bar\eta'_\alpha=\bar\eta_\beta(A^{-1})^\beta{}_\alpha$}
For the defining <SU(2)> action $\eta'=A\eta$, the conjugate row $\bar\eta_\alpha=(\eta^\alpha)^*$ transforms by $A^\dagger=A^{-1}$. Thus $\bar\eta_\alpha\eta^\alpha$ is invariant. The alternating <invariant tensor> $\epsilon_{12}=1$ satisfies $A^T\epsilon A=\epsilon$. Choose its inverse $\epsilon^{12}=-1$; then $\epsilon^{\alpha\gamma}\epsilon_{\gamma\beta}=\delta^\alpha{}_\beta$. Raising the conjugate index, $\widetilde\eta^\alpha=\epsilon^{\alpha\beta}\bar\eta_\beta$, gives another defining spinor. The resulting antilinear intertwiner squares to $-I$, so the defining representation is a <pseudoreal representation>.
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