A local Langlands correspondence and a categorical Hecke-algebra refinement are established for all non-singular depth-zero representations of reductive p-adic groups.
The explicit Local Langlands Correspondence for $\mathrm{GSp}_4$, $\mathrm{Sp}_4$ and stability (with an application to Modularity Lifting)
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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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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.