The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 (Annals of Mathematics Studies (129))

Bushnell, C., Kutzko, P. C.

ISBN 10: 0691032564 / ISBN 13: 9780691032566

Editore: Princeton University Press, 1994

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Codice articolo 178716

Dati bibliografici

• Titolo: The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 (Annals of Mathematics Studies (129))
• Editore: Princeton University Press
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 0691032564
• ISBN 13: 9780691032566
• Rilegatura: Rilegato
• Condizione: New

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Riassunto

This work gives a full description of a method for analyzing the admissible complex representations of the general linear groupG = 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 ofG. The authors define a family of representations of these compact open subgroups, which they callsimple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup ofG. 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 ofG, 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.