Definition
Morphism of Representations
A linear map $T : V \to W$ between $G$-representations (Definition~Group Representation) is a $G$-equivariant map (or intertwiner) if
\[
T \circ \rho_V(g) = \rho_W(g) \circ T \quad for all g \in G.
\]
An invertible intertwiner is an isomorphism of representations, analogous to a group isomorphism (Definition~Group Homomorphism).
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Dependency Graph
flowchart LR
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nca6bd350["Representation"]
ne087180c["Group Homomorphism"]
nf70e3a35["Morphism of Representations"]:::current
n36e5bd4f["Schur's Lemma"]
n8aabc776["Proposition"]
nca6bd350 --> nf70e3a35
ne087180c --> nf70e3a35
nf70e3a35 --> n36e5bd4f
nf70e3a35 --> n8aabc776
click nca6bd350 "../objects/ca6bd350.html" "_self"
click ne087180c "../objects/e087180c.html" "_self"
click n36e5bd4f "../objects/36e5bd4f.html" "_self"
click n8aabc776 "../objects/8aabc776.html" "_self"