---- Let $\text{GL}_{n}$ denote the [[general linear group]] over a [[field|field]] $\mathbb{F}$ (we assume $\mathbb{F}=\mathbb{C}$ whenever necessary). > [!definition] Definition. ([[Lie group representation]]) > A **representation** of a [[Lie group]] $G$ is a [[group representation|representation of]] $G$ whose defining [[group homomorphism|homomorphism]] $\rho:G \to \text{GL}_{n}$ is [[smooth]]. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```