  This paper provides a combinatorial dictionary between three sets of objects:
Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and the
irreducible modules of the affine Hecke algebra $H_n$ (for generic $q$).
  In particular, we compute the action of the crystal operator $\tilde{e}_i$ (a
refinement of socle of Restriction) on an irreducible module both in terms of
its parameterization by multisegments and by multipartitions. In other words,
we give explicit crystal graph isomorphisms.
  A byproduct is the determination of which multisegments parameterize modules
of the {\it cyclotomic} Hecke algebra $H_n^\lambda$. The theorems also explain
why the rule for computing $\tilde{e}_i$ mirrors the rule we know for that on a
tensor product of crystal graphs.
  We also give a construction of the irreducible module parameterized by a
multipartition without relying on a choice of path in the crystal graph.
  The proofs given here are elementary and do not rely on any geometry.
