BourbakiV1, Main, Exploration, bibRecord, 001248

Level Zero Types and Hecke Algebras for Local Central Simple Algebras

Identifieur interne : 001248 ( Main/Exploration ); précédent : 001247; suivant : 001249

Level Zero Types and Hecke Algebras for Local Central Simple Algebras

Auteurs : Martin Grabitz [Hongrie] ; Allan J. Silberger ; Ernst-Wilhelm Zink [Hongrie]

Source :

Journal of Number Theory [ 0022-314X ] ; 2001.

RBID : ISTEX:A9323E03C4006D4BFE3219239E1C2679406BB428

English descriptors

KwdEn :
- Algebra, Bernstein, Bernstein components, Bernstein spectrum, Bruhat, Bruhat decomposition, Bruhat representative, Bushnell, Cind, Conjugation, Coset, Cosets, Coxeter, Coxeter system, Cuspidal, Cuspidal level, Cuspidal pair, Cuspidal representation, Cuspidal representations, Divisor, Double coset, Double cosets, First factor, Galois, Galois group, Generalized tits system, Glsr, Grabitz, Hecke, Hecke algebra, Hecke algebras, Hereditary order, Homa, Irreducible, Irreducible cuspidal representation, Irreducible representation, Isomorphism, Iwahori, Kutzko, Levi, Levi factors, Levi subgroup, Local field, Main lemma, Matrix, Monomial matrices, Normalizes, Parabolic, Parabolic subgroup, Permutation, Permutation matrix, Prime element, Principal order, Proper parabolic subgroup, Residual, Residual field, Section fact, Silberger, Simple algebras, Split case, Subgroup, Supercuspidal, Supercuspidal support, Tensor, Tensor factors, Tensor product, Tensor products, Unipotent, Unramified, Zink.
Teeft :
- Algebra, Bernstein, Bernstein components, Bernstein spectrum, Bruhat, Bruhat decomposition, Bruhat representative, Bushnell, Cind, Conjugation, Coset, Cosets, Coxeter, Coxeter system, Cuspidal, Cuspidal level, Cuspidal pair, Cuspidal representation, Cuspidal representations, Divisor, Double coset, Double cosets, First factor, Galois, Galois group, Generalized tits system, Glsr, Grabitz, Hecke, Hecke algebra, Hecke algebras, Hereditary order, Homa, Irreducible, Irreducible cuspidal representation, Irreducible representation, Isomorphism, Iwahori, Kutzko, Levi, Levi factors, Levi subgroup, Local field, Main lemma, Matrix, Monomial matrices, Normalizes, Parabolic, Parabolic subgroup, Permutation, Permutation matrix, Prime element, Principal order, Proper parabolic subgroup, Residual, Residual field, Section fact, Silberger, Simple algebras, Split case, Subgroup, Supercuspidal, Supercuspidal support, Tensor, Tensor factors, Tensor product, Tensor products, Unipotent, Unramified, Zink.

Abstract

Abstract: Let D be a central division algebra and A×=GLm(D) the unit group of a central simple algebra over a p-adic field F. The purpose of this paper is to give types (in the sense of Bushnell and Kutzko) for all level zero Bernstein components of A× and to establish that the Hecke algebras associated to these types are isomorphic to tensor products of Iwahori Hecke algebras. The types which we consider are lifted from cuspidal representations τ of M(kD), where M is a standard Levi subgroup of GLm and kD is the residual field of D. Two types are equivalent if and only if the corresponding pairs (M(kD), τ) are conjugate with respect to A×. The results are basically the same as in the split case A×=GLn(F) due to Bushnell and Kutzko. In the non-split case there are more equivalent types and the proofs are technically more complicated.

Url:

https://api.istex.fr/document/A9323E03C4006D4BFE3219239E1C2679406BB428/fulltext/pdf

DOI: 10.1006/jnth.2001.2684

Affiliations:

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Le document en format XML

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<term>Bruhat decomposition</term>
<term>Bruhat representative</term>
<term>Bushnell</term>
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<term>Conjugation</term>
<term>Coset</term>
<term>Cosets</term>
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<term>Cuspidal</term>
<term>Cuspidal level</term>
<term>Cuspidal pair</term>
<term>Cuspidal representation</term>
<term>Cuspidal representations</term>
<term>Divisor</term>
<term>Double coset</term>
<term>Double cosets</term>
<term>First factor</term>
<term>Galois</term>
<term>Galois group</term>
<term>Generalized tits system</term>
<term>Glsr</term>
<term>Grabitz</term>
<term>Hecke</term>
<term>Hecke algebra</term>
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<term>Hereditary order</term>
<term>Homa</term>
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<term>Irreducible cuspidal representation</term>
<term>Irreducible representation</term>
<term>Isomorphism</term>
<term>Iwahori</term>
<term>Kutzko</term>
<term>Levi</term>
<term>Levi factors</term>
<term>Levi subgroup</term>
<term>Local field</term>
<term>Main lemma</term>
<term>Matrix</term>
<term>Monomial matrices</term>
<term>Normalizes</term>
<term>Parabolic</term>
<term>Parabolic subgroup</term>
<term>Permutation</term>
<term>Permutation matrix</term>
<term>Prime element</term>
<term>Principal order</term>
<term>Proper parabolic subgroup</term>
<term>Residual</term>
<term>Residual field</term>
<term>Section fact</term>
<term>Silberger</term>
<term>Simple algebras</term>
<term>Split case</term>
<term>Subgroup</term>
<term>Supercuspidal</term>
<term>Supercuspidal support</term>
<term>Tensor</term>
<term>Tensor factors</term>
<term>Tensor product</term>
<term>Tensor products</term>
<term>Unipotent</term>
<term>Unramified</term>
<term>Zink</term>
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<term>Bruhat decomposition</term>
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<term>Cuspidal pair</term>
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<term>Cuspidal representations</term>
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<term>Double cosets</term>
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<term>Parabolic subgroup</term>
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<term>Permutation matrix</term>
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<front><div type="abstract" xml:lang="en">Abstract: Let D be a central division algebra and A×=GLm(D) the unit group of a central simple algebra over a p-adic field F. The purpose of this paper is to give types (in the sense of Bushnell and Kutzko) for all level zero Bernstein components of A× and to establish that the Hecke algebras associated to these types are isomorphic to tensor products of Iwahori Hecke algebras. The types which we consider are lifted from cuspidal representations τ of M(kD), where M is a standard Levi subgroup of GLm and kD is the residual field of D. Two types are equivalent if and only if the corresponding pairs (M(kD), τ) are conjugate with respect to A×. The results are basically the same as in the split case A×=GLn(F) due to Bushnell and Kutzko. In the non-split case there are more equivalent types and the proofs are technically more complicated.</div>
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<country name="Hongrie"><region name="Berlin"><name sortKey="Grabitz, Martin" sort="Grabitz, Martin" uniqKey="Grabitz M" first="Martin" last="Grabitz">Martin Grabitz</name>
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<name sortKey="Zink, Ernst Wilhelm" sort="Zink, Ernst Wilhelm" uniqKey="Zink E" first="Ernst-Wilhelm" last="Zink">Ernst-Wilhelm Zink</name>
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Level Zero Types and Hecke Algebras for Local Central Simple Algebras

Level Zero Types and Hecke Algebras for Local Central Simple Algebras

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

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