Generic representations in L-packets

Abstract

We give the details of the construction of a map to restate a conjecture of Gan, Gross and Prasad about adjoint group action on generic representations in [Formula: see text]-packets. We give an application of the construction to give another proof of the classification of the Knapp–Stein [Formula: see text]-group associated to a unitary unramified character of a torus. Finally, we prove the conjecture for unramified [Formula: see text]-packets.