Dualizing Involutions on the n‐Fold Metaplectic Cover of GL(2)

Let be a non‐Archimedean local field of characteristic zero and . Let be a positive integer and be the ‐fold metaplectic cover of . Let be an irreducible smooth representation of and be the contragredient of . Let be an involutive anti‐automorphism of satisfying . In this case, we say that is a dualizing involution. When is the standard involution on , it is known that any lift of to the metaplectic double cover of is also dualizing. In this paper, we show that for , any lift of the standard involution to is never a dualizing involution.