This representation is called a bifundamental representation. For example, if u and v corresponds to S U ( 2 ) and S U ( 3 ) then the edge corresponds to a six-dimensional representation 2 ¯ ¯ SU ⁡ ⁡ ( 2 ) ⊗ ⊗ 3 SU ⁡ ⁡ ( 3 )