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Dual pairs and contragredients of irreducible representations

Dual pairs and contragredients of irreducible representations

Let G be one of the classical groups GL(n), U(n), O(n) or Sp(2n), over a nonarchimedean local field of characteristic zero.It is well known that the contragredient of an irreducible admissible smooth representation of G is isomorphic to a twist of it by an automorphism of G.We prove that similar …