Hi. I am currently studying about representations of Lie algebras. I have two questions: 1. As I understand, when we say a "representation" in the context of Lie algebras, we don't mean the matrices (with the appropriate Lie algebra) but rather the states on which they act. But then, the states contain less information than matrices, since there could be several representations (for a given dimension) acting on the same state. I am trying to understand why these states contain the same information as matrices. Is it because by "states" we actually mean weight vectors, which - in addition to containing vectors - contain the eigenvalues, so we could build up the matrices from them, and therefore they are equivalent to finding the generator matrices? 2. When we speak about "tensor representations" (for example, SU(n) tensors, which can also be described by Young Tableaux), what is their relation to the representations I mentioned in question 1 above? Thanks.