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Record Nr. |
UNINA9910154750803321 |
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Autore |
Bushnell C. |
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Titolo |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / / C. Bushnell, P. C. Kutzko |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1993 |
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ISBN |
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Descrizione fisica |
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1 online resource (327 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 311 |
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Classificazione |
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Disciplina |
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Soggetti |
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Representations of groups |
Nonstandard mathematical analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Introduction -- Comments for the reader -- 1. Exactness and intertwining -- 2. The structure of simple strata -- 3. The simple characters of a simple stratum -- 4. Interlude with Hecke algebra -- 5. Simple types -- 6. Maximal types -- 7. Typical representations -- 8. Atypical representations -- References -- Index of notation and terminology |
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Sommario/riassunto |
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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 |
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