Local Langlands Correspondence for Exceptional Groups over Function Fields

We establish a rigorous framework for the Local Langlands Correspondence (LLC) for split exceptional reductive groups G (specifically of types G2, F4, E6, E7, E8) over a non-archimedean local field F of positive characteristic p > 0. Building upon the seminal work of Genestier and V. Lafforgue on restricted shtukas and excursion operators, we construct a canonical map from the set of isomorphism classes of irreducible admissible representations of G(F) to the set of L-parameters : WF L G(C). We analyze the fibers of this map (L-packets) and discuss the compatibility with the explicit constructions for G2 via exceptional theta correspondences as proposed by Gan and Savin. Furthermore, we address the stability of L-packets and the preservation of local arithmetic invariants, providing a unified geometric approach to the LLC for exceptional groups in the equal characteristic setting.