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

Colin J. Bushnell; P. C. Kutzko

Published by Princeton University Press 1993

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

Colin J. Bushnell and P. C. Kutzko

Volume 129 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400882496

Overview
Contents

About this book

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.

Author / Editor information

Colin J. Bushnell is Professor of Mathematics at King's College, London. Philip C. Kutzko is Professor of Mathematics at the University of Iowa.

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Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	vii
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Comments for the reader Requires Authentication Unlicensed Licensed Download PDF	17
1. Exactness and intertwining Requires Authentication Unlicensed Licensed Download PDF	19
2. The structure of simple strata Requires Authentication Unlicensed Licensed Download PDF	49
3. The simple characters of a simple stratum Requires Authentication Unlicensed Licensed Download PDF	89
4. Interlude with Hecke algebra Requires Authentication Unlicensed Licensed Download PDF	143
5. Simple types Requires Authentication Unlicensed Licensed Download PDF	157
6. Maximal types Requires Authentication Unlicensed Licensed Download PDF	199
7. Typical representations Requires Authentication Unlicensed Licensed Download PDF	207
8. Atypical representations Requires Authentication Unlicensed Licensed Download PDF	265
References Requires Authentication Unlicensed Licensed Download PDF	307
Index of notation and terminology Requires Authentication Unlicensed Licensed Download PDF	311