The admissible dual of GL(N) via compact open subgroups

by Colin J. Bushnell and Philip C. Kutzko

This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the 'trivial type,' is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.

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書名 The admissible dual of GL(N) via compact open subgroups
著作者等 Bushnell, Colin J.
Kutzko, Philip C.
Kutzko Philip
Bushnell Colin J.
シリーズ名 Annals of mathematics studies
出版元 Princeton University Press
刊行年月 1993
ページ数 ix, 313 p.
大きさ 25 cm
ISBN 0691021147
NCID BA19262902
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言語 英語
出版国 アメリカ合衆国