The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / / C. Bushnell, P. C. Kutzko.
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 autho...
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Bushnell, C., author. aut http://id.loc.gov/vocabulary/relators/aut The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / C. Bushnell, P. C. Kutzko. Princeton, NJ : Princeton University Press, [2016] ©1993 1 online resource (332 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 129 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Nonstandard mathematical analysis. Representations of groups. MATHEMATICS / Algebra / Linear. bisacsh 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. Kutzko, P. C., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691021140 https://doi.org/10.1515/9781400882496 https://www.degruyter.com/isbn/9781400882496 Cover https://www.degruyter.com/document/cover/isbn/9781400882496/original |
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author |
Bushnell, C., Bushnell, C., Kutzko, P. C., |
spellingShingle |
Bushnell, C., Bushnell, C., Kutzko, P. C., The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / Annals of Mathematics Studies ; 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 |
author_facet |
Bushnell, C., Bushnell, C., Kutzko, P. C., Kutzko, P. C., Kutzko, P. C., |
author_variant |
c b cb c b cb p c k pc pck |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Kutzko, P. C., Kutzko, P. C., |
author2_variant |
p c k pc pck |
author2_role |
VerfasserIn VerfasserIn |
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Bushnell, C., |
title |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / |
title_full |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / C. Bushnell, P. C. Kutzko. |
title_fullStr |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / C. Bushnell, P. C. Kutzko. |
title_full_unstemmed |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / C. Bushnell, P. C. Kutzko. |
title_auth |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / |
title_alt |
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 |
title_new |
The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / |
title_sort |
the admissible dual of gl(n) via compact open subgroups. (am-129), volume 129 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (332 p.) Issued also in print. |
contents |
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 |
isbn |
9781400882496 9783110494914 9783110442496 9780691021140 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA171 |
callnumber-sort |
QA 3171 |
url |
https://doi.org/10.1515/9781400882496 https://www.degruyter.com/isbn/9781400882496 https://www.degruyter.com/document/cover/isbn/9781400882496/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512/.2 |
dewey-sort |
3512 12 |
dewey-raw |
512/.2 |
dewey-search |
512/.2 |
doi_str_mv |
10.1515/9781400882496 |
oclc_num |
979836554 |
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The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 / |
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