- Commit
- f9133eab0004eedb3be169e1ea72a3a5993c80f8
- Parent
- a3e69f1fe63270514bda5a81e1f10c7754c26b18
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Fixed a typo
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Fixed a typo
1 file changed, 1 insertion, 1 deletion
Status | File Name | N° Changes | Insertions | Deletions |
Modified | sections/semisimple-algebras.tex | 2 | 1 | 1 |
diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex @@ -531,7 +531,7 @@ establish\dots Now suppose that \(V\) is non-trivial, so that \(C_V\) acts on \(V\) as \(\lambda \operatorname{Id}\) for some \(\lambda \ne 0\). Given an eigenvalue - \(\mu \in K\) of the action of \(C\) in \(W\), denote by \(W^\mu\) its + \(\mu \in K\) of the action of \(C_V\) in \(W\), denote by \(W^\mu\) its associated generalized eigenspace. We claim \(W^0\) is the image of the inclusion \(K \to W\). Since \(C_V\) acts as zero in \(K\), this image is clearly contained in \(W^0\). On the other hand, if \(w \in W\) is such that