= Branching of a representation
The branching of a <group representation> $V$ to a <subgroup> $H$ is its decomposition into <irreducible representations> of $H$, when that <restriction of a representation> is a <semisimple representation>: $V|_H=\bigoplus_\lambda m_\lambda W_\lambda$. The nonnegative integers $m_\lambda$ are the branching multiplicities. For <finite groups> over the <complex numbers>, they are the <character inner products> of the restricted <character> with the <irreducible characters> of $H$. Restriction to an arbitrary <subgroup> need not be completely reducible.
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