On elliptic tempered characters
نویسنده
چکیده
Suppose that G(F) is a real or p-adic group. That is, G is a connected reductive algebraic group over a local field F, which we take to be of characteristic 0. Harmonic analysis on G(F) is built upon the set Htemp(G(F)) of irreducible tempered representations of G(F). These representations include the discrete series for G(F), and consist in general of irreducible constituents of representations induced from discrete series. We shall be interested in the subset of elliptic representations in IItemp(G(F)). The elliptic tempered representations also include the discrete series, and can be regarded as basic building blocks in HItemp(G(F)). The purpose of this paper is to study some properties of their characters. We should recall that in general a representation 7rEIItemp(G(F)) is infinite dimensional, and does not have a character in the classical sense. One of the cornerstones of
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