Functoriality for supercuspidal L-packets

TL;DR

This paper demonstrates that Kaletha's explicit supercuspidal L-packets for tame p-adic groups satisfy the fundamental functoriality property expected in the Local Langlands Correspondence, confirming their theoretical consistency.

Contribution

It proves the functoriality of Kaletha's explicitly constructed supercuspidal L-packets, a key property for the Local Langlands Correspondence.

Findings

Kaletha's L-packets satisfy the functoriality property

Explicit descriptions of supercuspidal representations are used

Supports the conjectural framework of the Local Langlands Correspondence

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.