Strong multiplicity one theorems for affine Hecke algebras of type A

Given an irreducible module for the affine Hecke algebraH_n of type A, we consider its restriction toH_n–1. We prove that the socle of restriction is multiplicity free and moreover that the summands lie in distinct blocks. This is true regardless of the characteristic of the field or of the order of the parameterq in the definition ofH_n. The result generalizes and implies the classical branching rules that describe the restriction of an irreducible representation of the symmetric groupS_n toS_n–1.Both authors would like to thank Gus Lehrer and the University of Sydney for their hospitality while this paper was edited into its final form.