lie-algebras-and-their-representations

diff --git a/sections/preface.tex b/sections/preface.tex
@@ -28,9 +28,8 @@ will be covered in the notes as needed.
 
 This document was typeset and compiled using free software. Its \LaTeX~source
 code is freely available at
-\url{https://git.pablopie.xyz/lie-algebras-and-their-representations/README.html},
-for distribution under the terms of the Creative Commons Attribution 4.0
-license.
+\url{https://git.pablopie.xyz/lie-algebras-and-their-representations}, for
+distribution under the terms of the Creative Commons Attribution 4.0 license.
 
 I would like to thank my family for their tireless love and support. I would
 specially like to thank professor Kashuba and Eduardo Monteiro Mendonça for

diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -78,10 +78,10 @@ around \(\lambda\).
 Our main objective is to show \(V\) is determined by this string of
 eigenvalues. To do so, we suppose without any loss in generality that
 \(\lambda\) is the right-most eigenvalue of \(h\), fix some nonzero \(v \in
-V_\lambda\) and consider the set \(\{v, f v, f^2, v, \ldots\}\).
+V_\lambda\) and consider the set \(\{v, f v, f^2 v, \ldots\}\).
 
 \begin{proposition}\label{thm:basis-of-irr-rep}
-  The set \(\{v, f v, f^2, \ldots\}\) is a basis for \(V\). In addition, the
+  The set \(\{v, f v, f^2 v, \ldots\}\) is a basis for \(V\). In addition, the
   action of \(\mathfrak{sl}_2(K)\) on \(V\) is given by the formulas
   \begin{equation}\label{eq:irr-rep-of-sl2}
     \begin{aligned}
@@ -102,7 +102,7 @@ V_\lambda\) and consider the set \(\{v, f v, f^2, v, \ldots\}\).
 
   The fact that \(h f^k v \in K \langle v, f v, f^2 v, \ldots \rangle\) follows
   immediately from our previous assertion that \(f^k v \in V_{\lambda - 2 k}\)
-  -- indeed, \(h f^k v = (\lambda - 2 k) f^k v \in K \langle v, f v, f^2, v,
+  -- indeed, \(h f^k v = (\lambda - 2 k) f^k v \in K \langle v, f v, f^2 v,
   \ldots \rangle\), which also goes to show one of the formulas in
   (\ref{eq:irr-rep-of-sl2}). Seeing \(e f^k v \in K \langle v, f v, f^2 v,
   \ldots \rangle\) is a bit more complex. Clearly,