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).
Read more about this topic: Local Langlands Conjectures
Famous quotes containing the words local, conjectures and/or groups:
“Reporters for tabloid newspapers beat a path to the park entrance each summer when the national convention of nudists is held, but the cult’s requirement that visitors disrobe is an obstacle to complete coverage of nudist news. Local residents interested in the nudist movement but as yet unwilling to affiliate make observations from rowboats in Great Egg Harbor River.”
—For the State of New Jersey, U.S. public relief program (1935-1943)
“After all, it is putting a very high price on one’s conjectures to have a man roasted alive because of them.”
—Michel de Montaigne (1533–1592)
“Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.”
—Zick Rubin (20th century)