The admissible dual of GL(N) via compact open subgroups
Author(s)
Bibliographic Information
The admissible dual of GL(N) via compact open subgroups
（Annals of mathematics studies, no. 129）
Princeton University Press, 1993
- : pbk
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Hiroshima University Central Library, Interlibrary Loan
411.6:B-95/HL4010004000404782,
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:512/b9642070249535
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Note
Includes bibliographical references (p. 307-310) and index
Description and Table of Contents
- Volume
-
: pbk ISBN 9780691021140
Description
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.
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
- Volume
-
ISBN 9780691032566
Description
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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