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

Key Points

• The aim is to provide a simple proof of the existence of automorphisms in p-adic classical groups and similitude groups that dualize representations.
• Utilized concepts from Tupan to frame the proof.
• Explored dual representations in classical groups and similitude groups.
• Applied the results broadly across many p-adic classical groups.
• Demonstrated the existence of automorphisms that map irreducible smooth representations to their duals.
• Established that the proof holds for classical and similitude groups under certain conditions.
• Noted that the approach does not apply in cases with even residual characteristic.

Abstract