  Strong evidence indicates that the spectrum of planar anomalous dimensions of
N=4 super Yang-Mills theory is given asymptotically by Bethe equations. A
curious observation is that the Bethe equations for the psu(1,1|2) subsector
lead to very large degeneracies of 2^M multiplets, which apparently do not
follow from conventional integrable structures. In this article, we explain
such degeneracies by constructing suitable conserved nonlocal generators acting
on the spin chain. We propose that they generate a subalgebra of the loop
algebra for the su(2) automorphism of psu(1,1|2). Then the degenerate
multiplets of size 2^M transform in irreducible tensor products of M
two-dimensional evaluation representations of the loop algebra.
