- #1

- 22

- 1

_{a}} be the set of generators of su(N), a = 1, ..., N

^{2}- 1. The action of the adjoint representation of U on some generator t

_{a}can be written as

Ad(U)t

_{a}= Λ(U)

_{ab}t

_{b}

I want to characterize the matrix Λ(U), i. e., I want to see which of its elements are independent. It's known that it belongs to a subspace of SO(N

^{2}- 1), and we can derive some constraints by saying that the adjoint action respects the Lie bracket. Here https://mathoverflow.net/questions/179032/characterising-the-adjoint-representation-of-sun it says that the most general characteristic of the adjoint representation is that it preserves some 3-form, but I can't find the details (I don't really know what am I looking for). Does you guys know some place where I can find details about this kind of characterization of the adjoint representation for compact groups? Thanks!