Functoriality for supercuspidal L-packets

Abstract

Kaletha constructs $L$-packets for supercuspidal $L$-parameters of tame $p$-adic groups. These $L$-packets consist entirely of supercuspidal representations, which are explicitly described. Using the explicit descriptions, we show that Kaletha's $L$-packets satisfy a fundamental functoriality property desired for the Local Langlands Correspondence.

Extended to prove a more precise functoriality conjecture of Solleveld for regular supercuspidal L-parameters and to include fields of positive characteristic