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\begin{equation*}
  \alignedat 2
  J_{st}^s(\theta) &= 
    \bmatrix \xi_1 & \xi_2' & \cdots & \xi_n' \endbmatrix
    &\qquad
    \xi_i' &= \operatorname{Ad}_{\bigl(
      \displaystyle
      e^{\widehat{\xi}_1 \theta_1} \cdots e^{\widehat{\xi}_{i-1} \theta_{i-1}}
    \bigr)} \xi_i \\
  J_{st}^b(\theta) &=
    \bmatrix 
      \xi_1^\dagger & \cdots & \xi_{n-1}^\dagger & \xi_n^\dagger 
    \endbmatrix &\qquad 
    \xi_i^\dagger &= \operatorname{Ad}^{-1}_{\bigl(
      \displaystyle 
      e^{\widehat{\xi}_i \theta_i} \cdots e^{\widehat{\xi}_n \theta_n} g_{st}(0)
    \bigr)} \xi_i.
  \endaligned
\end{equation*}
\end{document}