lie-algebras-and-their-representations

Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules

Commit
6cdd06ed443b2db6cb94def42abd64f326f7975a
Parent
50666a027d221c87a1ca943b229a85f42b4f6a94
Author
Pablo <pablo-escobar@riseup.net>
Date

Changed the styling of a weight diagram

Diffstats

1 files changed, 4 insertions, 4 deletions

Status Name Changes Insertions Deletions
Modified sections/sl2-sl3.tex 2 files changed 4 4 
diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -893,17 +893,17 @@ weight of \(V\) we started with.
       \draw[very thick] \weight{-5}{5} -- \weight{5}{-5};
       \draw[very thick] \weight{0}{-5} -- \weight{0}{5};
       \draw[very thick] \weight{-5}{0} -- \weight{5}{0};
-      \draw[gray, thick] \weight{1}{2} -- \weight{-2}{-1};
+      \draw[dashed, thick] \weight{1}{2} -- \weight{-2}{-1};
       \wt[black]{1}{2}
       \wt[black]{-2}{-1}
-      \wt{0}{1}
-      \wt{-1}{0}
+      \wt[black]{0}{1}
+      \wt[black]{-1}{0}
     \end{rootSystem}
   \end{tikzpicture}
 \end{center}
 
 By construction, \(\nu\) corresponds to the right-most weight of the
-representation of \(\mathfrak{sl}_2(K)\), so that all dots lying on the gray
+representation of \(\mathfrak{sl}_2(K)\), so that all dots lying on the dashed
 string must occur in the representation of \(\mathfrak{sl}_2(K)\). Hence they
 must also be weights of \(V\). The final picture is thus
 \begin{center}