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

Bushnell, Colin J.; Kutzko, Philip

doi:10.1515/9781400882496

Cited by 317 publications

(1,210 citation statements)

References 0 publications

Supporting

Mentioning

1,040

Contrasting

Unclassified

121

Order By: Relevance

“…The proof is very much along the lines of [6] (8.1.5), though the geometry causes some extra complications. We know already, from [14] §1.…”

Section: Introductionmentioning

confidence: 94%

“…Note that, in the case E = F , this is not the same definition as in [6] (1.4.5) (k 0 (β, Λ) = −∞ there). If e(Λ|o E ) denotes the o E -period of Λ, then k 0 (β, Λ)/e(Λ|o E ) is an integer independent of the choice of Λ; we denote it k F (β).…”

Section: Stratamentioning

confidence: 99%

“…We refer the reader to [6], [7], [12], [13] for more details on the results recalled in this section.…”

Section: Preliminariesmentioning

confidence: 99%

“…As in [7], we will allow the indices in the filtration to be real numbers, by putting a n = a n , for n ∈ R. Note also that, for n ∈ Z, the integers n 2 + 1 and n+1 2 often appear in [6], [7] etc. ; with the notation as here, we have a n 2 +1 = a n 2 + , and a n+1 2 = a n 2 .…”

Section: Stratamentioning

confidence: 99%

“…One of the main ingredients in the description of the admissible dual of G by Bushnell and Kutzko ( [6], [7]) is the notion of simple characters: these are arithmetically defined characters of certain compact open subgroups of G. To obtain all the irreducible supercuspidal representations of G in [6], there are three main steps: first, to show that these simple characters have some rather remarkable properties of functoriality (and it turns out that they even have such properties when the dimension N is allowed to vary (see [6], [10]) and similarly for the base field F (see [4], [5] and sequels); second, to show that any irreducible supercuspidal representation of G contains a simple character θ of a group denoted H 1 ; and finally, to find the representations of the normalizer in G of θ which contain θ.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Semisimple characters for p-adic classical groups

Stevens¹

2005

Duke Math. J.

102

View full text Add to dashboard Cite

Let G be a unitary, symplectic or orthogonal group over a non-archimedean local field of residual characteristic different from 2, considered as the fixed point subgroup in a general linear group G of an involution. Following [7] and [13], we generalize the notion of a semisimple character for G and for G. In particular, following the formalism of [4], we show that these semisimple characters have certain functorial properties. Finally, we show that any positive level supercuspidal representation of G contains a semisimple character.

show abstract

“…The proof is very much along the lines of [6] (8.1.5), though the geometry causes some extra complications. We know already, from [14] §1.…”

Section: Introductionmentioning

confidence: 94%

Section: Stratamentioning

confidence: 99%

“…We refer the reader to [6], [7], [12], [13] for more details on the results recalled in this section.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Stratamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Semisimple characters for p-adic classical groups

Stevens¹

2005

Duke Math. J.

102

View full text Add to dashboard Cite

show abstract

Continuation of Hereditary Orders in Local Central Simple Algebras

Grabitz

1999

Journal of Number Theory

View full text Add to dashboard Cite

More on Embeddings of Local Fields in Simple Algebras

Zink¹

1999

Journal of Number Theory

View full text Add to dashboard Cite

Let A | F be a central simple algebra over a p-field F of arbitrary characteristic. Then concretely A may be represented as a complete m_m matrix algebra A=M m (D d ), where D d =D denotes a central division algebra of index d over F. Thus the reduced degree of A over F is N=dm. 1 We write o F , respectively O D , for the ring of integers of F, respectively D, and P F =? F o F , respectively P D =? D O D , for the maximal ideals of o F , respectively O D . We write k F , respectively k D , for the residual fields of F and D.An o F -order of A is any subring of A containing the identity element of A which is also a finitely generated o F submodule of A containing an F basis for A. Let A denote an o F -order of A. We call A hereditary [R, p. 27] if every left ideal of A is a projective left A module. The order A has a Jacobson radical P A [R, p. 77ff ]; it is the minimal (two-sided) ideal of A such that the quotient ring AÂP A is semi-simple. If A is hereditary, then AÂP A is a direct product of complete matrix algebras with entries in k D , and ? F A=P rd A with a positive integer r, called the period of A. Following Benz [B], Bushnell and Fro hlich [BF], and Fro hlich [F] we callThe period of a principal order A determines A up to conjugacy. If A is principal with period r, then A is conjugate to the standard principal order A r /M r (M s (O D )) such that the r_r matrix g=( g ij ) belongs to A r if and only if g ij # M s (P D ) for i> j. Thus the set of standard principal orders A r of A, and hence the set of conjugacy classes of principal orders of A, corresponds bijectively to the set of factors r of m.

show abstract

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

Cited by 317 publications

References 0 publications

Semisimple characters for p-adic classical groups

Semisimple characters for p-adic classical groups

Continuation of Hereditary Orders in Local Central Simple Algebras

More on Embeddings of Local Fields in Simple Algebras

Contact Info

Product

Resources

About