The local Langlands correspondence of essentially unipotent supercuspidal representations for disconnected reductive groups

Abstract

We construct the local Langlands correspondence of essentially unipotent supercuspidal representations under the framework of rigid inner forms and prove a certain functoriality and compatibilities. This is stronger than an analogous result of Solleveld, which did not care about rigidifications of inner twists. We also generalize this correspondence for disconnected reductive groups. We expect to use this result for extension of Kaletha's explicit local Langlands correspondence of non-singular supercuspidal representations.