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

git clone: git://git.pablopie.xyz/lie-algebras-and-their-representations
Log
Files
Refs
README
LICENSE

Commit: 9900613a5470181a5ebd150ab216dcaea7acda4d
Parent: 1ff40e693033cdde49668288bfac8f899a03ee1e
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 4 Jan 2023 18:04:28 +0000

Changed the notation for differential operators

Diffstat

1 file changed, 3 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	6	3	3

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -689,9 +689,9 @@ century. Specifically, we find\dots
 \begin{proposition}\label{thm:geometric-realization-of-uni-env}
   Let \(G\) be a Lie group and \(\mathfrak{g}\) be its Lie algebra. Denote by
   \(\operatorname{Diff}(G)^G\) the algebra of \(G\)-invariant differential
-  operators in \(G\) -- i.e. the algebra of all differential operators \(L :
-  C^\infty(G) \to C^\infty(G)\) such that \((L(f \circ \ell_g)) \circ
-  \ell_{g^{-1}} = L f\) for all \(f \in C^\infty(G)\) and \(g \in G\). There is
+  operators in \(G\) -- i.e. the algebra of all differential operators \(P :
+  C^\infty(G) \to C^\infty(G)\) such that \((P(f \circ \ell_g)) \circ
+  \ell_{g^{-1}} = P f\) for all \(f \in C^\infty(G)\) and \(g \in G\). There is
   a canonical isomorphism of algebras \(\mathcal{U}(\mathfrak{g}) \isoto
   \operatorname{Diff}(G)^G\).
 \end{proposition}