Strong multiplicity one theorems for affine Hecke algebras of type A
DPMMS Centre for Mathematical Sciences
Department of MathematicsUniversity of California at San Diego
Cite this article as:
Grojnowski, I. & Vazirani, M. Transformation Groups (2001) 6: 143. doi:10.1007/BF01597133
Given an irreducible module for the affine Hecke algebraHn of type A, we consider its restriction toHn−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 ofHn. The result generalizes and implies the classical “branching rules” that describe the restriction of an irreducible representation of the symmetric groupSn toSn−1.