There are some things wrong with the simple quark model discussed in the previous chapter. The first is that the connection between spin and statistics is wrong for these quarks. The quarks must have spin 1/2 in order to produce the spin 1/2 and 3/2 baryons. Thus we would expect them to obey Fermi-Dirac statistics, and we would expect the ground state of the three quark system to be an s-wave, completely symmetric under the exchange of the position labels of the three quarks. This would lead to an SU(6) representation completely antisymmetric in the SU(6) indices of the three quarks — which is a  or a 20 which transforms under SU(3) × SU(2) as ([2, 1], [2, 1]) ⊕ (, [1, 1, 1]) or (8, 2) ⊕ (1, 4) which is not what we want.