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Self-dual representations of some dyadic groups
Authors:Colin J Bushnell  Guy Henniart
Institution: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
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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