A. Zee, Quantum Field Theory in a Nutshell · Problem VII.7.5

Field Theory Redux

Physics — QFT

Problem

The group

SO(6)

has

6(6-1)/2 = 15

generators. Notice that the group

SU(4)

also has

4^2 - 1 = 15

generators. Substantiate your suspicion that

SO(6)

and

SU(4)

are isomorphic. Identify some low dimensional representations.