Local Langlands Conjectures For Other Groups
Borel (1979) and Vogan (1993) discuss the Langlands conjectures for more general groups. As of 2011, the Langlands conjectures for arbitrary reductive groups G are not as precise as the ones for general linear groups, and it is unclear what the correct way of stating them should be. Roughly speaking, admissible representations of a reductive group are grouped into disjoint finite sets called L-packets, which should correspond to some classes of homomorphisms, called L-parameters, from the Weil–Deligne group to the L-group of G.
Langlands (1989) proved the Langlands conjectures for groups over the archimedean local fields R and C by giving the Langlands classification of their irreducible admissible representations (up to infinitesimal equivalence), or, equivalently, of their irreducible -modules.
Gan & Takeda (2011) proved the local Langlands conjectures for the symplectic similitude group GSp(4) and used that in Gan & Takeda (2010) to deduce it for the symplectic group Sp(4).
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