Motivated by an answer to this mathoverflow question I've been making an effort to understand Baez and Huerta's article "The algebra of grand unified theories".

As far as I can tell, mathematically, the first 30 pages or so describe one concrete finite dimensional representation of the group $U(1)\times SU(2)\times SU(3)$. The vectors of this space are to be interpreted as the elementary particles which do not mediate forces (i.e. fermions) and their anti-particles, while composed particles (made up of several fermions and anti-fermions) are represented by vectors of tensor powers of this space which must satisfy some additional conditions (such as being fixed by the action of elements in $1 \times 1 \times SU(3)$). Finally, the elementary force mediating particles (elementary Bosons) are represented by elements of the Lie algebra of the group.

Assuming I've got that right there are still some phrases which make absolutely no sense to me, or worse, I can make sense of them only as completely trivial statements. The most extreme example I can find is the following (page 490 third paragraph):

"... in 1936 a paper by Cassen and Condon appeared suggesting that the nucleon’s Hilbert space $\mathbb{C}^2$ is acted on by the symmetry group $SU(2)$."

The literal interpretation is that Cassen and Condon suggested that it is possible to multiply a $2\times 2$ matrix with a $2\times 1$ vector. Obviously this can't be what that authors intended to communicate.

**So my question is: What's the meaning of this phrase?**

The paper refered to is "On nuclear forces" from Phys. Rev. 50 (1936) which I don't have access to. From this page it seems they proposed some model accounting for the experimental fact that the strong nuclear force doesn't depend on the electrical charge of the particles involved. I still don't get it. Any help?