The Admissible Dual of Gl(n) Via Compact Open Subgroups. (Am-129) by Colin J. Bushnell

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Author
Colin J. Bushnell
Publisher
Princeton University Press
Date of release
Pages
313
ISBN
9780691032566
Binding
Hardcover
Illustrations
Format
PDF, EPUB, MOBI, TXT, DOC
Rating
5
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Book review


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.



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