I would be glad if someone can help me understand the argument in the first paragraph of page 4 of this paper.
Especially I don't understand their first sentence,
"Using N bosons (fermions) distributed over m states, one can construct completely symmetric (antisymmetric) irreducible representations of the group U(m) associated with Young tableaux with N boxes in a row (column)"
(I am quite familiar with the Quantum Statistics concepts being alluded to but not so much with the Young-Tableux technology being used)
All I can see is that $U(n)$ can act on the space of $c_i$ and keep the operators defined in their equation 2.9 and 2.10 unchanged.
Also on page 4 is there a typo in Equation 2.13? It doesn't seem to follow from the line previous to it and the line previous to it makes no sense to me. I guess there should have been a "=" between the $\lambda^N$ and $exp$ in the line just before 2.13.
Even if I make the above "correction" I don't see how 2.13 follows from it.