lie-algebras-and-their-representations

diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -75,7 +75,7 @@ combinatorial counterpart.
   associated with the weight \(\lambda\)}.
 \end{definition}
 
-% TODO: Define the dot-action beforehand
+% TODO: Cite the definition of the dot action
 \begin{theorem}[Harish-Chandra]
   Given \(\lambda, \mu \in \mathfrak{h}^*\), \(\chi_\lambda = \chi_\mu\) if,
   and only if \(\mu \in W \bullet \lambda\). All algebra homomorphism
@@ -137,7 +137,7 @@ Example~\ref{ex:sp-canonical-basis}.
         )
   \end{align*}
   is \(W\)-equivariant bijection, where the action \(W \cong S_n \ltimes
-  (\mathbb{Z}/2\mathbb{Z})^n\) on \(\mathfrak{h}^*\) is given by the dot-action
+  (\mathbb{Z}/2\mathbb{Z})^n\) on \(\mathfrak{h}^*\) is given by the dot action
   and the action of \(W\) on \(K^n\) is given my permuting coordinates and
   multiplying them by \(\pm 1\). A weight \(\lambda \in \mathfrak{h}^*\)
   satisfies the conditions of Lemma~\ref{thm:sp-bounded-weights} if, and
@@ -217,7 +217,7 @@ Example~\ref{ex:sl-canonical-basis}.
         )
   \end{align*}
   is \(W\)-equivariant bijection, where the action \(W \cong S_n\) on
-  \(\mathfrak{h}^*\) is given by the dot-action and the action of \(W\) on the
+  \(\mathfrak{h}^*\) is given by the dot action and the action of \(W\) on the
   space of \(\mathfrak{sl}_n\)-sequences is given my permuting coordinates. A
   weight \(\lambda \in \mathfrak{h}^*\) satisfies the conditions of
   Lemma~\ref{thm:sl-bounded-weights} if, and only if the diferences between all