diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -291,15 +291,15 @@ Example~\ref{ex:sp-canonical-basis}. Also fix \(\rho = \sfrac{1}{2} \beta_1 +
\begin{align*}
\mathfrak{h}^* & \to K^n \\
\lambda &
- \mapsto (\kappa(\epsilon_1, \lambda), \ldots, \kappa(\epsilon_1, \lambda))
+ \mapsto (\kappa(\epsilon_1, \lambda), \ldots, \kappa(\epsilon_n, \lambda))
\end{align*}
is equivariant with respect to the natural action of \(W\) on
\(\mathfrak{h}^*\). But this also clear from the isomorphism \(W \cong S_n
\ltimes (\mathbb{Z}/2\mathbb{Z})^n\), as described in
Example~\ref{ex:sp-weyl-group}: \((\sigma_i, (\bar 0, \ldots, \bar 0)) =
\sigma_{\beta_i}\) permutes \(\epsilon_i\) and \(\epsilon_{i + 1}\) for \(i <
- n\) and \((1, (\bar 0, \ldots, \bar 0, \bar 1) = \sigma_{\beta_n}\) flips the
- sign of \(\epsilon_n\). Hence \(m(\sigma_{\beta_i} \cdot \epsilon_j) =
+ n\) and \((1, (\bar 0, \ldots, \bar 0, \bar 1)) = \sigma_{\beta_n}\) flips
+ the sign of \(\epsilon_n\). Hence \(m(\sigma_{\beta_i} \cdot \epsilon_j) =
\sigma_{\beta_i} \cdot m(\epsilon_j)\) for all \(i\) and \(j\). Since \(W\)
is generated by the \(\sigma_{\beta_i}\), this implies that the required map
is equivariant.