By Armand Borel

Half 1 includes sections on Reductive teams, representations, Automorphic types and representations)

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Extra info for Automorphic forms, representations, and L-functions, Part 1

Sample text

2]). 1 . The apartment of a maximal split torus and the affine root system. 1 . 1 . The split case. As a motivation for what follows, we first consider the case where Go is split, that is, where S is a maximal torus of G. Then, the groups Ua are K-isomorphic to the additive group. Indeed, the choice of a "Chevalley basis" in the Lie algebra of G determines a system of K-isomorphisms Xa : Add -> Ua (an "epinglage") satisfying the commutation relations of Chevalley [10, p. 27]. Since K is a local field, its additive group is filtered and so are the groups Ua(K), "par transport de structure".

68 0. Preliminaries. 0. Introduction. This is a survey of some aspects of the structure theory of reduc­ I. tive groups over local fields.

43 2. The building . . . 2. 1 . Definitions . . . 2. / . 44 .. . . 3. Metric and simplicial decomposition . . . 4. Dynkin diagram ; special and hyperspecial points . 5. / and Ll ; conjugacy classes of special and 46 hyperspecial points .

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