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

Parameterizing Hecke Algebra Modules: Bernstein-Zelevinsky Multisegments, Kleshchev Multipartitions, and Crystal Graphs