Definition:Dimension (Representation Theory)
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Definition
Let $\struct {k, +, \circ}$ be a field.
Let $V$ be a vector space over $k$ of finite dimension.
Let $\GL V$ be the general linear group of $V$.
Let $\struct {G, \cdot}$ be a finite group.
Let $\rho: G \to \GL V$ be a linear representation of $G$ on $V$.
The dimension or degree of $\rho$, written $\map \deg \rho$ is the dimension of the vector space $V$.