The Admissible Dual of Gl (Annals of Mathematics Studies, Band 129) - Hardcover
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This work gives a full description of a method for analyzing the admissible complex representations of the general linear groupG = 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 ofG. The authors define a family of representations of these compact open subgroups, which they callsimple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup ofG. 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 ofG, 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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Colin J. Bushnell is Professor of Mathematics at King's College, London. Philip C. Kutzko is Professor of Mathematics at the University of Iowa.
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The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 (Annals of Mathematics Studies (129))
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The admissible dual of GL(N) via compact open subgroups / by Colin J. Bushnell and Philip C. Kutzko
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Princeton, N.J. : Princeton University Press, 1993
ISBN 10: 0691032564
ISBN 13: 9780691032566
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First Edition. Fine paperback copy. Particularly and surprisingly well-preserved; tight, bright, clean and especially sharp-cornered. Physical description; ix, 313 pages : illustrations. Notes; Includes bibliographical (pages 307-310) references and index. Contents; Comments for the reader -- 1. Exactness and intertwining. (1.1). Hereditary orders. (1.2). Hereditary orders relative to subfields. (1.3). Tame corestriction. (1.4). Adjoint maps. (1.5). Simple strata and intertwining. (1.6). The simple intersection property -- 2. The structure of simple strata. (2.1). Equivalence of pure strata. (2.2). Refinements of simple strata. (2.3). Split refinements. (2.4). Approximation of simple strata. (2.5). Nonsplit fundamental strata. (2.6). Intertwining and conjugacy -- 3. The simple characters of a simple stratum. (3.1). The rings of a simple stratum. (3.2). Characters and commutators. (3.3). Intertwining. (3.4). A nondegeneracy property. (3.5). Intertwining and conjugacy. (3.6). Change of rings -- 4. Interlude with Hecke algebras. (4.1). Induction and intertwining. (4.2). Scalar Hecke algebras. (4.3). Unitary structures -- 5. Simple types. (5.1). Heisenberg representations. (5.2). Extending to level zero. (5.3). A bound on intertwining. (5.4). Affine Hecke algebras and Weyl groups. (5.5). Intertwining and Weyl groups. (5.6). The Hecke algebra of a simple type. (5.7). Intertwining and conjugacy for simple types -- 6. Maximal types. (6.1). Extension by a central character. (6.2). Supercuspidal representations -- 7. Typical representations. (7.1). Some Iwahori decompositions. (7.2). Iwahori factorisation of a simple type. (7.3). Main theorems. (7.4). Proof of the principal lemma. (7.5). The strong intertwining property. (7.6). Jacquet functors and Hecke algebra maps. (7.7). Discrete series and formal degree -- 8. Atypical representations. (8.1). Split types. (8.2). Jacquet module of a split type I. (8.3). Jacquet module of a split type II. (8.4). The main theorems. (8.5). Classification -- Index of notation and terminology. Subjects; Representations of groups. Nonstandard mathematical analysis. MATHEMATICS Algebra Linear. 3 Kg. Artikel-Nr. 432779
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