The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 (eBook)

Colin J. Bushnell, P. C. Kutzko (Autoren)

eBook Download: PDF

2016
332 Seiten
Princeton University Press (Verlag)
978-1-4008-8249-6 (ISBN)

Infos

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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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 "e;trivial type,"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: 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 • Dimension (vector space) • Discrete series representation • Discrete valuation ring • Divisor • Eigenvalues and Eigenvectors • equivalence class • exactness • exact sequence • 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 Field • Local Langlands conjectures • 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 • SUBGROUP • Subquotient • Subset • Support (mathematics) • Symmetric group • tensor product • Terminology • Theorem • topological group • Topology • Vector Space • Weil group • Weyl Group
• ISBN-10: 1-4008-8249-4 / 1400882494
• ISBN-13: 978-1-4008-8249-6 / 9781400882496