lie-algebras-and-their-representations

diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -91,12 +91,15 @@ combinatorial counterpart.
   Then \(\chi_\lambda = \chi_\mu\).
 \end{proposition}
 
-% TODO: Note that if σ_β ∙ λ is not dominant integral then L(σ_β ∙ λ) is
-% infinite-dimensional and 𝓔𝔁𝓽(L(σ_β ∙ λ)) ≅  𝓔𝔁𝓽(L(λ))
+% TODO: Remark that the probability of σ_β ∙ λ ∈ P+ is slight: there precisely
+% one eleement in the orbit of λ which is dominant integral
 \begin{proposition}\label{thm:lemma6.1}
-  Let \(\beta \in \Sigma\) and \(\lambda \notin P^+\) be such that
+  Let \(\beta \in \Sigma\) and \(\lambda \notin P^+\) be such that.
   \(L(\lambda)\) is bounded and \(\lambda(H_\beta) \notin \mathbb{N}\). Then
-  \(L(\sigma_\beta \bullet \lambda) \subset \mExt(L(\lambda))\).
+  \(L(\sigma_\beta \bullet \lambda) \subset \mExt(L(\lambda))\). In particular,
+  if \(\sigma_\beta \bullet \lambda \notin P^+\) then \(L(\sigma_\beta)\) is a
+  bounded infinite-dimensional \(\mathfrak{g}\)-module and
+  \(\mExt(L(\sigma_\beta \bullet \lambda)) \cong \mExt(L(\lambda))\).
 \end{proposition}
 
 % TODOO: Treat the case of sl(2) here?