Definition 32.1.2 (Left Regular Representation).label Let $G$ be a locally compact group, then the mapping
\[\pi_{L}: G \to U(B(L^{2}(G))) \quad x \mapsto L_{x}\]
is the left regular representation of $G$.
Definition 32.1.2 (Left Regular Representation).label Let $G$ be a locally compact group, then the mapping
is the left regular representation of $G$.
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