The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / / C. Bushnell, P. C. Kutzko

• Autore: Bushnell C.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1993
• Descrizione fisica: 1 online resource (327 pages) : illustrations
• Disciplina: 512/.2
• Soggetto topico: Representations of groups; Nonstandard mathematical analysis
• Soggetto non controllato: Abelian group; Abuse of notation; Additive group; Affine Hecke algebra; Algebra homomorphism; Approximation; Automorphism; Bijection; Block matrix; Calculation; Cardinality; Classical group; Computation; Conjecture; Conjugacy class; Contradiction; Corollary; Coset; Critical exponent; Diagonal matrix; Dimension (vector space); Dimension; Discrete series representation; Discrete valuation ring; Divisor; Eigenvalues and eigenvectors; Equivalence class; Exact sequence; Exactness; Existential quantification; Explicit formula; Explicit formulae (L-function); Field extension; Finite group; Functor; Gauss sum; General linear group; Group theory; Haar measure; Harmonic analysis; Hecke algebra; Homomorphism; Identity matrix; Induced representation; Integer; Irreducible representation; Isomorphism class; Iwahori subgroup; Jordan normal form; Levi decomposition; Local Langlands conjectures; Local field; Locally compact group; Mathematics; Matrix coefficient; Maximal compact subgroup; Maximal ideal; Multiset; Normal subgroup; P-adic number; Permutation matrix; Polynomial; Profinite group; Quantity; Rational number; Reductive group; Representation theory; Requirement; Residue field; Ring (mathematics); Scientific notation; Simple module; Special case; Sub"ient; Subgroup; Subset; Support (mathematics); Symmetric group; Tensor product; Terminology; Theorem; Topological group; Topology; Vector space; Weil group; Weyl group
• Classificazione: SK 340
• Persona (resp. second.): KutzkoP. C.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- Contents -- Introduction -- Comments for the reader -- 1. Exactness and intertwining -- 2. The structure of simple strata -- 3. The simple characters of a simple stratum -- 4. Interlude with Hecke algebra -- 5. Simple types -- 6. Maximal types -- 7. Typical representations -- 8. Atypical representations -- References -- Index of notation and terminology
• Sommario/riassunto: 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.
• Titolo autorizzato: The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129
• ISBN: 1-4008-8249-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154750803321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 129.