Fixed a few small errors in rep thry of fin gps.

Class Notes/Algebra/representation-theory-of-finite-groups.tex

@@ -1673,7 +1673,8 @@ \section{Mackey Theory}
   \tr \rho^3(srs) = \tr \rho^3(r^{-1}) = -1 = \tr \rho^3(r)\), so
   \(\Ind_{\Z_4}^{D_8} 
   \rho^3\) will \emph{not} be irreducible. On the other hand, one can
-  check \(\rho^2_s(r) = \rho^2(srs) = \rho^2(r^{-1}) = -i = \rho^4(r)\), so
+  check \(\tr \rho^2_s(r) = \tr \rho^2(srs) = \tr \rho^2(r^{-1}) = -i
+  = \tr \rho^4(r)\), so
   \(\rho^2_s\) and \(\rho^2\) are orthogonal, thus sharing no
   irreducibles. Thus, it must be that \(\Ind_{\Z_4}^{D_8} \rho^2\) is
   irreducible. In fact, one can check \(\Ind_{\Z_4}^{D_8} \rho^2 =
@@ -1940,7 +1941,7 @@ \section{Example: Representations of the Symmetric Group}
     \end{ytableau}
   \]
   Furthermore, \(\Sym_n\) can act on a Young tableau by permuting the
-  numbers. So, \((12345)(876)(9,10) \in \Sym_10\) would act on the
+  numbers. So, \((12345)(876)(9,10) \in \Sym_{10}\) would act on the
   above diagram to yield \[
     \begin{ytableau}
       2 & 3 & 4 & 5 & 1\\
@@ -1989,7 +1990,7 @@ \section{Example: Representations of the Symmetric Group}
     Q(\T) := \sum_{\alpha \in C(\T)} \sgn(\alpha) \alpha
   \]
 \end{defn}
-
+\todo{Finish this to give some idea of irreducibles.}
 \begin{bibdiv}
   \begin{biblist}
     \bib{benson}{book}{