I have a very basic query about multiplets. In the SU(3) approach strongly interacting particles, quarks and hadrons are the basis vectors of irreducible representations of SU(3). Now, quarks and hadrons are definite properties with define eigenvalues of hypercharge and isospin: to put it another way, there is only one set of quarks and hadrons. But there are many different irreducible representations of SU(3). For example, we are free to choose the Cartan representation, or the Gell-Mann representation, of the SU(3) matrices as our representation of SU(3). How do we know that these different representations will all produce particles with the same set of eigenvalues of isospin and hypercharge - ie, how do we know whatever representation we choose, we'll get back our actual quarks and the hadrons? Any help would be appreciated. Thanks!