Transformation Groups

, Volume 6, Issue 2, pp 143–155

Strong multiplicity one theorems for affine Hecke algebras of type A

  • I. Grojnowski
  • M. Vazirani

DOI: 10.1007/BF01597133

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.

Copyright information

© Birkhäuser 2001

Authors and Affiliations

  • I. Grojnowski
    • 1
  • M. Vazirani
    • 2
  1. 1.DPMMS Centre for Mathematical SciencesCambridgeUK
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA