adjoint()

Rep syten::Rep::adjoint

(

)

const

Returns the adjoint of this irrep.

In our use, the adjoint of an irrep A is the irrep B where the vacuum irrep is contained in the product decomposition of A and B.

• For U(1), the adjoint is the group with the negative label (e.g. charge 1 → charge -1, (1) × (-1) → (0))
• For SU(2), irreps are self-adjoint (e.g. spin S=1 → spin S=1, (1) × (1) → [(2), (0)])
• For SU(3), I have no idea.
• For Z/n, the adjoint of an element m is n-m, s.t. the sum of both gives n, i.e. 0.

References group.