 Flavour singlet of three scalar quarks

If three quarks are hypothetically spin-zero bosons, their total state is symmetric under particle exchange. In an $L=0$ symmetric spatial state, the unchanged antisymmetric three-quark colour singlet therefore requires an antisymmetric quark flavour state. With three flavours its space is ${\bigwedge }^3{\mathbb{C}}^3$, of dimension one. The sole flavour state contains one quark of each flavour and has total angular momentum zero.