The Admissible Dual of GL(N) via Compact Open Subgroups (Annals of Mathematics Studies) - Colin J. Bushnell, Philip C. Kutzko (1993)
ISBN 0691032564
Subject Nonstandard mathematical analysis; Representations of groups
Publisher Princeton University Press
Publication Date February 1993
Format Hardcover (248 x 165 mm)
Language e
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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Collection Status In Collection
Index 517
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Product Details
LoC Classification QA171 .B978 1993 copy 1
Dewey 512/.2
Cover Price $80.00
No. of Pages 332