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

責任表示 by Colin J. Bushnell and Philip C. Kutzko
シリーズ Annals of mathematics studies ; no. 129
データ種別 図書
出版者 Princeton, N.J. : Princeton University Press
出版年 1993
本文言語 英語
大きさ ix, 313 p. ; 25 cm
概要 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 structur... 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.
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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所蔵情報


理系図3F 数理独自 068222193001948 BUSH/30/1 1993

書誌詳細

一般注記 Includes bibliographical references (p. 307-310) and index
著者標目 *Bushnell, Colin J. (Colin John), 1947-
Kutzko, Philip C., 1946-
件 名 LCSH:Representations of groups
LCSH:Nonstandard mathematical analysis
分 類 LCC:QA171
DC20:512/.2
NDC8:411.6
書誌ID 1000030424
ISBN 0691032564
NCID BA19262902
巻冊次 ISBN:0691032564 ; PRICE:$59.50
: pbk ; ISBN:0691021147 ; PRICE:$24.95
登録日 2009.09.10
更新日 2009.11.02

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