Admissible Dual of GL(N) via Compact Open Subgroups
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A01=Colin J. Bushnell
A01=P. C. Kutzko
A01=Philip C. Kutzko
Abelian group
Additive group
Affine Hecke algebra
Algebra homomorphism
Author_Colin J. Bushnell
Author_P. C. Kutzko
Author_Philip C. Kutzko
Automorphism
Block matrix
Cardinality
Category=PBF
Category=PBG
Classical group
Computation
Conjecture
Conjugacy class
Coset
Diagonal matrix
Dimension
Dimension (vector space)
Discrete series representation
Divisor
Eigenvalues and eigenvectors
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivalence class
Exact sequence
Exactness
Explicit formula
Explicit formulae (L-function)
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
Locally compact group
Matrix coefficient
Maximal compact subgroup
Maximal ideal
Multiset
Normal subgroup
P-adic number
Permutation matrix
Polynomial
Profinite group
Rational number
Reductive group
Representation theory
Residue field
Ring (mathematics)
Scientific notation
Simple module
Special case
Subgroup
Subquotient
Subset
Symmetric group
Tensor product
Theorem
Topological group
Topology
Vector space
Weil group
Weyl group
Product details
- ISBN 9780691021140
- Weight: 454g
- Dimensions: 152 x 235mm
- Publication Date: 03 Jan 1993
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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 "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.
Colin J. Bushnell is Professor of Mathematics at King's College, London. Philip C. Kutzko is Professor of Mathematics at the University of Iowa.
