Color-ordered amplitudes for the scattering of n particles in the adjointrepresentation of SU(N) gauge theory satisfy constraints that arise from grouptheory alone. These constraints break into subsets associated with irreduciblerepresentations of the symmetric group S_n, which allows them to be presentedin a compact and natural way. Using an iterative approach, we derive theconstraints for six-point amplitudes at all loop orders, extending earlierresults for n=4 and n=5. We then decompose the four-, five-, and six-pointgroup-theory constraints into their irreducible S_n subspaces. We commentbriefly on higher-point two-loop amplitudes.
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