Automorphic forms, representations, and L-functions, Part 1 by Armand Borel

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By Armand Borel

Half 1 comprises sections on Reductive teams, representations, Automorphic kinds and representations)

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

Sample text

4. 1 . Introduction . . . . . . 2. Residually split groups . 4. 3 . 4. Interpretation . . 5. I nvariants . . . 6. The classification kit . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Lwahori and H. Matsumoto [15], who were considering split semisimple groups, that quasi-split and classical groups were later on studied by H . Hijikata [13], and that, in the generality given here, most results are due to F. Bruhat and the author [6], [7], [8], [9]. For further information, one may consult the introduction of [8]. 2. Notations. The following notations will be used throughout the paper : K denotes a field endowed with a nontrivial discrete valuation w, the value group no with 7r E l1 w(K x ) ( c R) is also called r.

30 30 30 1 . The apartment of a maximal split torus and the affine root system 31 31 1 . 1 . The split case . 2. The apartment A(G, S, K) . . . . 31 32 1 . 3. Remark . .. . 4. Filtration of the groups Ua (K) . . . 33 1 . 5. 6. 7. Half-apartments, chambers, affine Weyl group 1 . 8 . 9. Root system attached to a point of A and special points . . . 35 1 . 10. Behaviour under field extension and hyperspecial points .

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