  We determine the scaling limit for permutations conditioned to have longest
decreasing subsequence of length at most $d$. These permutations are also said
to avoid the pattern $(d+1)d \cdots 2 1$ and they can be written as a union of
$d$ increasing subsequences. We show that these increasing subsequences can be
chosen so that, after proper scaling, and centering, they converge in
distribution. As the size of the permutations tends to infinity, the
distribution of functions generated by the permutations converges to the
eigenvalue process of a traceless $d\times d$ Hermitian Brownian bridge.
