If one iterates the multiplicity-free branching rule from $\operatorname{GL}(n)$ representations (finite-dim, over $\mathbb C$) to $\operatorname{GL}(n-1)$ all the way down to $\operatorname{GL}(0)$, one obtains triangular "Gel'fand-Cetlin (or Zeitlin or Tseytlin or...) patterns", indexing a basis of the representation. The differences in the row sums indicates the weight of the basis element.
If one only iterates $b$ times (for $n=a+b$), this gives a branching law from $\operatorname{GL}(a+b)$ to $\operatorname{GL}(a) \times \operatorname{GL}(1)^b$, in terms of Gel'fand-Cetlin trapezoids of height $b$. Using the crystal structure on SSYT, in bijection with GC patterns, one should be able to make these trapezoids into a $\operatorname{GL}(b)$ crystal.
What are the highest-weight Gel'fand-Cetlin trapezoids, giving a branching law from $\operatorname{GL}(a+b)$ to $\operatorname{GL}(a)\times\operatorname{GL}(b)$?
As the above suggests, I think answering this is a matter of following bijections -- I just would rather quote a reference than reinvent the wheel. (Probably p385 of Zhelobenko's book? I don't have access to the whole thing, and the snippet Google provides has too much undefined notation for me to readily compare to GC patterns. If I'm reading correctly, he only gives a positive formula for fundamental representations, and uses a determinant to give a nonpositive formula in general.)
