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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Admissible Dual of Gl(n) Via Compact Open Subgroups. (Am-129), Volume 129

The Admissible Dual of Gl(n) Via Compact Open Subgroups. (Am-129), Volume 129

Bushnell, Colin J.
Kutzko, Philip C.

Paperback

Series: Annals of Mathematics Studies, Book 129

AlgebraGeneral Mathematics

ISBN10: 0691021147
ISBN13: 9780691021140
Publisher: Princeton University Press
Published: Jan 3 1993
Pages: 332
Weight: 1.05
Height: 0.81 Width: 6.12 Depth: 9.26
Language: English

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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