Representation ring of a compact group
= Representation ring of a compact group
{title2=$R(G)$}
The representation ring is the <Grothendieck group> of finite-dimensional complex <unitary representations> of a <compact group>, with addition induced by <direct sum> and multiplication by <tensor product>. As an abelian group it is freely generated by the irreducible <unitary representations>. Taking dimension gives a ring homomorphism $R(G)\to\mathbb Z$.