Self-dual representations of some dyadic groups |
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Authors: | Colin J. Bushnell Guy Henniart |
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Affiliation: | 1.Department of Mathematics,King’s College London,London,UK;2.Laboratoire de Mathématiques d’Orsay,Université de Paris-Sud,Orsay Cedex,France;3.CNRS,Orsay Cedex,France |
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Abstract: | Let F be a non-Archimedean local field of residual characteristic two and let d be an odd positive integer. Let D be a central F-division algebra of dimension d 2. Let π be one of: an irreducible smooth representation of D × , an irreducible cuspidal representation of GL d (F), an irreducible smooth representation of the Weil group of F of dimension d. We show that, in all these cases, if π is self-contragredient then it is defined over mathbb Q{mathbb Q} and is orthogonal. We also show that such representations exist. |
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