The Admissible Dual of GL(N) via Compact Open Subgroups

Colin J. Bushnell

ISBN 10: 0691021147 / ISBN 13: 9780691021140

Published by Princeton University Press, 1993

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Bibliographic Details

• Title: The Admissible Dual of GL(N) via Compact Open Subgroups
• Publisher: Princeton University Press
• Publication Date: 1993
• Language: English
• ISBN 10: 0691021147
• ISBN 13: 9780691021140
• Binding: PAP
• Condition: New
• Weight: 533 grams

About this title

Synopsis

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.

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.