The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / / C. Bushnell, P. C. Kutzko.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Bushnell, C.,; Kutzko, P. C.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1993
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 129
• Physical Description: 1 online resource (332 p.)

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.

Table of Contents

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