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

Format:

Book

Author/Creator:

Bushnell, C., author.

Kutzko, P. C., author.

Series:

Annals of mathematics studies ; no. 129.

Annals of Mathematics Studies ; 311

Language:

English

Subjects (All):

Representations of groups.

Nonstandard mathematical analysis.

Physical Description:

1 online resource (327 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

Summary:

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.

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

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882496

1400882494

OCLC:

979836554