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Journal of Lie Theory 27 (2017), No. 2, 419--434
Copyright Heldermann Verlag 2017

Dualizing Involutions for Classical and Similitude Groups over Local Non-Archimedean Fields

Alan Roche
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019-3103, U.S.A.

C. Ryan Vinroot
Dept. of Mathematics, College of William and Mary, P.O. 8795, Williamsburg, VA 23187-8795, U.S.A.

Building on ideas of Tupan, we give an elementary proof of a result of Moeglin, Vignéras 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.

Keywords: Classical and similitude groups, involution, dual representation, Cayley maps.

MSC: 22E50, 20G05

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