Dualizing involutions for classical and similitude groups over local   non-archimedean fields
  Building on ideas of Tupan, we give an elementary proof of a result of M{\oe}glin, Vign\'{e}ras 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. 
Alan Roche and C. Ryan Vinroot
math.RT