Definition:Dimension (Representation Theory)

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 $V$.