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Extension Du Formalisme De Bushnell Et Kutzko Au Cas D'une Algèbre À Division
Author(s) -
Broussous P
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000471
Subject(s) - mathematics , mathematics subject classification , extension (predicate logic) , formalism (music) , pure mathematics , dual (grammatical number) , combinatorics , algebra over a field , art , musical , literature , computer science , visual arts , programming language
Bushnell and Kutzko gave a complete and effective classification of the smooth dual of GL( N, F ), where F is a non‐archimedean local field. Similarly, Zink gave a classification of the smooth dual of D × , where D is a division algebra with centre F , in terms of non‐canonical objects and under the restrictive hypothesis that F has characteristic 0. In this paper, we extend part of Bushnell and Kutzko's formalism to D × and obtain a complete classification of the smooth dual working for any characteristic. The crucial point of this work is to define a good way of splitting the algebra D so that the important notion of simple stratum , and its properties, can be translated to D × by some descent arguments. 1991 Mathematics Subject Classification : 12E15, 20G05, 20G25, 22E50.