What I want, with manual alignment:
\begin{equation*}
\begin{cases}
\ang{\varphi} \rightarrow \Omega_n\\
\varphi^k \hspace{4.4pt}\mapsto \xi_n^k
\end{cases}
\end{equation*}
With align I get unwanted space:
\begin{align*}
\begin{cases}
\ang{\varphi} &\rightarrow \Omega_n\\
\varphi^k &\mapsto \xi_n^k
\end{cases}
\end{align*}



caseswhich is not for aligning at relation signs, but for aligning conditions – egreg Jun 07 '21 at 16:10