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Strong multiplicity one theorems for affine Hecke algebras of type A

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Abstract

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.

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Authors and Affiliations

  1. DPMMS Centre for Mathematical Sciences, Wilberforce Road, CB3 0WB, Cambridge, UK

    I. Grojnowski

  2. Department of Mathematics, University of California at San Diego, 9500 Gilman Drive 0112, 92093-0112, La Jolla, CA, USA

    M. Vazirani

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  1. I. Grojnowski
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  2. M. Vazirani
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Additional information

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.

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Grojnowski, I., Vazirani, M. Strong multiplicity one theorems for affine Hecke algebras of type A. Transformation Groups 6, 143–155 (2001). https://doi.org/10.1007/BF01597133

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  • DOI: https://doi.org/10.1007/BF01597133

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