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

by Colin J. Bushnell, P. C. Kutzko

Overview

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.

Product Details

ISBN-13:	9780691021140
Publisher:	Princeton University Press
Publication date:	01/03/1993
Series:	Annals of Mathematics Studies , #129
Pages:	332
Product dimensions:	6.00(w) x 9.25(h) x (d)

About the Author

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

Table of Contents

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