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This work establishes a surjection linking irreducible representations to Langlands parameters, suggesting new insights into local Langlands conjectures.
We construct a surjection from the set of irreducible representations of SLN(k), where k is a finite field, to the set of inertia equivalence classes of tame Langlands parameters for SLN(F), where F is a p-adic field with residue field k. We provide a parametrization of the fibers, establishing a conjecture formulated by Imai and Vogan. Additionally, we examine the compatibility of this surjection with the Local Langlands Correspondence for SLN(F), confirming a related conjecture of Vogan. This work extends several results previously established for GLN.
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Elena Collacciani (2025) studied this question.
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