lie-algebras-and-their-representations

diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -105,7 +105,8 @@ of diagonal matrices, as in Example~\ref{ex:cartan-of-sp}, and the basis
 \epsilon_i - \epsilon_{i+1}\) for \(i < n\) and \(\beta_n = 2 \epsilon_n\).
 Here \(\epsilon_i : \mathfrak{h} \to K\) is the linear functional which yields
 the \(i\)-th entry of the diagonal of a given matrix, as described in
-Example~\ref{ex:sp-canonical-basis}.
+Example~\ref{ex:sp-canonical-basis}. Also fix \(\rho = \sfrac{1}{2} \beta_1 +
+\cdots + \sfrac{1}{2} \beta_n\).
 
 \begin{lemma}\label{thm:sp-bounded-weights}
   Then \(L(\lambda)\) is bounded if, and only if
@@ -169,7 +170,8 @@ diagonal matrices, as in Example~\ref{ex:cartan-of-sl}, and the basis \(\Sigma
 \epsilon_i - \epsilon_{i+1}\) for \(i < n\). Here \(\epsilon_i : \mathfrak{h}
 \to K\) is the linear functional which yields the \(i\)-th entry of the
 diagonal of a given matrix, as described in
-Example~\ref{ex:sl-canonical-basis}.
+Example~\ref{ex:sl-canonical-basis}. Also fix \(\rho = \sfrac{1}{2} \beta_1 +
+\cdots + \sfrac{1}{2} \beta_{n - 1}\).
 
 % TODO: Add some comments on the proof of this: while the proof that these
 % conditions are necessary is a purely combinatorial affair, the proof of the