- Commit
- 09fea928cc0a047acfe95545325b75d75a14d0a9
- Parent
- 20117e2e20c0f2eb66b41e4a837fcf5e33ce02ba
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Minor tweak in notation
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, 3 insertions, 3 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | sections/simple-weight.tex | 6 | 3 | 3 |
diff --git a/sections/simple-weight.tex b/sections/simple-weight.tex @@ -109,8 +109,8 @@ to the case it holds. This brings us to the following definition. (M_1 \otimes M_2)_{\lambda_1 + \lambda_2} = (M_1)_{\lambda_1} \otimes (M_2)_{\lambda_2} \] - for all \(\lambda_i \in \mathfrak{h}_i^*\) and \(\operatorname{supp} M_1 - \otimes M_2 = \operatorname{supp} M_1 \oplus \operatorname{supp} M_2 = \{ + for all \(\lambda_i \in \mathfrak{h}_i^*\) and \(\operatorname{supp} (M_1 + \otimes M_2) = \operatorname{supp} M_1 \oplus \operatorname{supp} M_2 = \{ \lambda_1 + \lambda_2 : \lambda_i \in \operatorname{supp} M_i \subset \mathfrak{h}_i^*\}\). \end{example} @@ -184,7 +184,7 @@ A particularly well behaved class of examples are the so called a bounded \(\mathfrak{g}\)-module with \(\deg M_1 \otimes M_2 = \deg M_1 \cdot \deg M_2\) and \[ - \operatorname{supp}_{\operatorname{ess}} M_1 \otimes M_2 + \operatorname{supp}_{\operatorname{ess}} (M_1 \otimes M_2) = \operatorname{supp}_{\operatorname{ess}} M_1 \oplus \operatorname{supp}_{\operatorname{ess}} M_2 = \{