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A Reduction over finite fields of the tame local Langlands correspondence for SLn
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We establish a conjecture formulated by Vogan for SLn. Specifically, we construct a surjection from the set of irreducible representations of SLn(k), where k is a finite field, to the inertia equivalence classes of tame Langlands parameters for SLn(F), where F is a p-adic field with residue field k. Additionally, we provide a parametrization of the fibers of this surjection and examine its compatibility with the Local Langlands Correspondence for SLn. This work extends several results previously established for GLn to the context of SLn.
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Finite Langlands correspondence
Every irreducible representation of a connected reductive group over a finite field is matched with a special Langlands parameter, with the fiber over each parameter given by irreducible representations of a finite co...
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