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MR2485462 (2010h:11087) 11F70 (19F15 22E41 22E50)
Weissman, Martin H. (1UCSC)
Metaplectic tori over local fields. (English summary)
Pacific J. Math. 241 (2009), no. 1, 169200.
Let T be an algebraic torus over a local field F and let T = T(F). Let L/F be a finite Galois
extension, with Galois group , over which T splits. By a result of Langlands, the group of
continuous characters of T, denoted by H(T), is naturally isomorphic to H1
c (WL/F , T), where
WL/F is the Weil group of L/F, T is the complex dual torus of T and H1
c is the continuous
group cohomology. Now let T be the central extension of T by ľn = nth roots of unity. Let
denote a fixed injective character of ľn. A continuous genuine character of T is an element
of H(T) which restricts to . An irreducible representation of T is said to be genuine if the
center acts via a continuous genuine character. Let I(T) denote the set of irreducible genuine
representations of T. The main theorem of the paper, under some assumptions, parametrizes
I(T) in a way that generalizes the result of Langlands: there exists a finitetoone map from
