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The explicit Local Langlands Correspondence for $\mathrm{GSp}_4$, $\mathrm{Sp}_4$ and stability (with an application to Modularity Lifting)

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arxiv 2304.02622 v2 pith:D2WEC5RI submitted 2023-04-05 math.NT math.RT

Kenta Suzuki , Yujie Xu This is my paper · ORCID
classification math.NTmath.RT
keywords localmathrmcorrespondenceexplicitgivelanglandsapplicationlifting
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abstract

We give a purely local proof of the explicit Local Langlands Correspondence for $\mathrm{GSp}_4$ and $\mathrm{Sp}_4$. Moreover, we give a unique characterization in terms of stability of $L$-packets and other properties. Finally, in the appendix, we give an application of our explicit local Langlands correspondence to modularity lifting.

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  1. Hecke algebras and local Langlands correspondence for non-singular depth-zero representations

    math.RT 2024-11 conditional novelty 7.0 of 10

    A local Langlands correspondence and a categorical Hecke-algebra refinement are established for all non-singular depth-zero representations of reductive p-adic groups.

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