Dualizing involutions for classical and similitude groups over local non-archimedean fields

Abstract

Building on ideas of Tupan, we give an elementary proof of a result of Mœglin, Vignéras and Waldspurger on the existence of automorphisms of many $p$-adic classical groups that take each irreducible smooth representations to its dual. Our proof also applies to the corresponding similitude groups.

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• Self-dual representations of Sp(4,F)