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
854e67bcff0ee44a2d07eba9b3068fa65c2ccf5d
Parent
9c254f28439268d83e9e55efc47a440391717f32
Author
Pablo <pablo-escobar@riseup.net>
Date

Removed a stupid epigraph

Diffstat

1 file changed, 4 insertions, 8 deletions

Status File Name N° Changes Insertions Deletions
Modified sections/sl2-sl3.tex 12 4 8
diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -1,8 +1,5 @@
 \chapter{Representations of \(\mathfrak{sl}_2(K)\) and \(\mathfrak{sl}_3(K)\)}
 
-% TODO: Remove this?
-\epigraph{Nobody has ever bet enough on a winning horse.}{Some gambler}
-
 % TODOOOO: Write an intetroduction!
 
 \section{Representations of \(\mathfrak{sl}_2(K)\)}\label{sec:sl2}
@@ -38,11 +35,10 @@ of \(V\) -- where \(\lambda\) ranges over the eigenvalues of \(h\) and
 \(V_\lambda\) is the corresponding eigenspace. At this point, this is nothing
 short of a gamble: why look at the eigenvalues of \(h\)?
 
-The short answer is that, as we shall see, this will pay off -- which
-conveniently justifies the epigraph of this chapter. For now we will postpone
-the discussion about the real reason of why we chose \(h\). Let \(\lambda\) be
-any eigenvalue of \(h\). Notice \(V_\lambda\) is in general not a
-subrepresentation of \(V\). Indeed, if \(v \in V_\lambda\) then
+The short answer is that, as we shall see, this will pay off. For now we will
+postpone the discussion about the real reason of why we chose \(h\). Let
+\(\lambda\) be any eigenvalue of \(h\). Notice \(V_\lambda\) is in general not
+a subrepresentation of \(V\). Indeed, if \(v \in V_\lambda\) then
 \begin{align*}
   h e v & =   2e v + e h v = (\lambda + 2) e v \\
   h f v & = - 2f v + f h v = (\lambda - 2) f v