An analysis reveals automorphisms that dualize representations in classical and similitude groups over p-adic fields, suggesting broader implications for group theory.
Building on ideas of Tupan, we give an elementary proof of a result of Moeglin, Vignras and Waldspurger on the existence of automorphisms of many p-adic classical groups that take each irreducible smooth representation to its dual.Our proof also applies to the corresponding similitude groups.It does not apply in even residual characteristic.
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Roche et al. (2017) studied this question.
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