- Commit
- 02ff7321bcae84e4056fc4e8f275d8b6c9c94b56
- Parent
- d2c1e21e268cd01331407b312ab6f851c8340753
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Fixed a TODO item
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
Diffstat
1 file changed, 4 insertions, 5 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | sections/semisimple-algebras.tex | 9 | 4 | 5 |
diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex @@ -792,8 +792,6 @@ Moreover, we find\dots \end{align*} In the language of the diagrams used in chapter~\ref{ch:sl3}, we write - % TODO: Add a label to the righ of the diagram indicating that the top arrows - % are the action of e and the bottom arrows are the action of f \begin{center} \begin{tikzcd} \cdots \arrow[bend left=60]{r}{-10} @@ -804,9 +802,10 @@ Moreover, we find\dots & M(\lambda)_2 \arrow[bend left=60]{l}{1} \end{tikzcd} \end{center} - where \(M(\lambda)_{2 - 2 k} = K f^k v\). In this case, unlike we have see in - chapter~\ref{ch:sl3}, the string of weight spaces to left of the diagram is - infinite. + where \(M(\lambda)_{2 - 2 k} = K f^k v\). Here the top arrows represent the + action of \(e\) and the bottom arrows represent the action of \(f\). In this + case, unlike we have see in chapter~\ref{ch:sl3}, the string of weight spaces + to left of the diagram is infinite. \end{example} What's interesting to us about all this is that we've just constructed a