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October 22, 2025Open Access

A Reduction Over Finite Fields of the Tame Local Langlands Correspondence for SLN

Key Points

A surjection maps irreducible representations of SLN(k) to Langlands parameters for SLN(F), extending known results.
This research confirms conjectures by Imai, Vogan, and shows compatibility with local Langlands correspondence.
Parametrization of the fibers is provided, enhancing our understanding of the relationships between these mathematical structures.
This study builds on previous work on GLN, indicating deeper structural connections within representation theory.

Abstract

Abstract We construct a surjection from the set of irreducible representations of SL₍ (k), where k is a finite field, to the set of inertia equivalence classes of tame Langlands parameters for SL₍ (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 SL₍ (F), confirming a related conjecture of Vogan. This work extends several results previously established for GL₍.

A Reduction Over Finite Fields of the Tame Local Langlands Correspondence for SLN

Key Points

Abstract

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