05981nam 22015375 450 991015475080332120190708092533.01-4008-8249-410.1515/9781400882496(CKB)3710000000622804(MiAaPQ)EBC4738792(DE-B1597)467956(OCoLC)979836554(DE-B1597)9781400882496(EXLCZ)99371000000062280420190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierThe Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 /C. Bushnell, P. C. KutzkoPrinceton, NJ : Princeton University Press, [2016]©19931 online resource (327 pages) illustrationsAnnals of Mathematics Studies ;3110-691-02114-7 Includes bibliographical references and index.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 terminologyThis 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.Annals of mathematics studies ;no. 129.Representations of groupsNonstandard mathematical analysisAbelian 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.Representations of groups.Nonstandard mathematical analysis.512/.2SK 340rvkBushnell C., 1126189Kutzko P. C., DE-B1597DE-B1597BOOK9910154750803321The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 1292657528UNINA