A local Langlands correspondence and a categorical Hecke-algebra refinement are established for all non-singular depth-zero representations of reductive p-adic groups.
Functoriality for supercuspidal L-packets
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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.
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2024 1verdicts
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Hecke algebras and local Langlands correspondence for non-singular depth-zero representations
A local Langlands correspondence and a categorical Hecke-algebra refinement are established for all non-singular depth-zero representations of reductive p-adic groups.