Example
Regular Representation
The regular representation of $G$ is the action of $G$ on the group
algebra $k[G]$ by left multiplication (a special case of Group Representation):
\[
\rho(g) \cdot \sum_{h \in G} a_h \, h \;=\; \sum_{h \in G} a_h \, (gh).
\]
By Maschke's Theorem, over an algebraically closed field of characteristic zero,
every irreducible representation appears in $k[G]$ with multiplicity equal to
its degree.
Dependency Graph
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