Colin J. Bushnell
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Colin J. Bushnell has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Guy Henniart
Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France
9 shared publications - Freydoon Shahidi
Purdue University
1 shared publication - Henry H. Kim
Department of Mathematics, University of Toronto, Toronto, Canada
1 shared publication Philip C. Kutzko
King‘s College
1 shared publication- Philip C. Kutzko
Department of Mathematics, University of Iowa, Iowa City, IA52242, USA
1 shared publication
Latest Publications
- 21 June 2005
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 141 (04) , 979-1011
The essentially tame local Langlands correspondence, II: totally ramified representations
The essentially tame local Langlands correspondence, II: totally ramified representations - Volume 141 Issue 4 - Colin J. Bushnell, Guy Henniart
- 21 June 2005
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 141 (04) , 979-1011
The essentially tame local Langlands correspondence, II: totally ramified representations
The essentially tame local Langlands correspondence, II: totally ramified representations - Volume 141 Issue 4 - Colin J. Bushnell, Guy Henniart
- 25 April 2005
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 18 (3) , 685-710
The essentially tame local Langlands correspondence, I
Let F F be a non-Archimedean local field (of characteristic 0 0 or p p ) with finite residue field of characteristic p p . An irreducible smooth representation of the Weil group of F F is called essentially tame if its restriction to wild inertia is a sum of characters. The set of isomorphism classes of irreducible, essentially tame representations of dimension n n is denoted G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) . The Langlands correspondence induces a bijection of G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) with a certain set A n e t ( F ) \mathcal {A}^\mathrm {et}_n(F) of irreducible supercuspidal representations of G L n ( F ) \mathrm {GL}_n(F) . We consider the set P n ( F ) P_n(F) of isomorphism classes of certain pairs ( E / F , ξ ) (E/F,\xi ) , called “admissible”, consisting of a tamely ramified field extension E / F E/F of degree n n and a quasicharacter ξ \xi of E × E^\times . There is an obvious bijection of P n ( F ) P_n(F) with G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) . Using the classification of supercuspidal representations and tame lifting, we construct directly a canonical bijection of P n ( F ) P_n(F) with A n e t ( F ) \mathcal {A}^\mathrm {et}_n(F) , generalizing and simplifying a construction of Howe (1977). Together, these maps give a canonical bijection of G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) with A n e t ( F ) \mathcal {A}^\mathrm {et}_n(F) . We show that one obtains the Langlands correspondence by composing the map P n ( F ) → A n e <mi...
- 25 April 2005
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 18 (3) , 685-710
The essentially tame local Langlands correspondence, I
Let F F be a non-Archimedean local field (of characteristic 0 0 or p p ) with finite residue field of characteristic p p . An irreducible smooth representation of the Weil group of F F is called essentially tame if its restriction to wild inertia is a sum of characters. The set of isomorphism classes of irreducible, essentially tame representations of dimension n n is denoted G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) . The Langlands correspondence induces a bijection of G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) with a certain set A n e t ( F ) \mathcal {A}^\mathrm {et}_n(F) of irreducible supercuspidal representations of G L n ( F ) \mathrm {GL}_n(F) . We consider the set P n ( F ) P_n(F) of isomorphism classes of certain pairs ( E / F , ξ ) (E/F,\xi ) , called “admissible”, consisting of a tamely ramified field extension E / F E/F of degree n n and a quasicharacter ξ \xi of E × E^\times . There is an obvious bijection of P n ( F ) P_n(F) with G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) . Using the classification of supercuspidal representations and tame lifting, we construct directly a canonical bijection of P n ( F ) P_n(F) with A n e t ( F ) \mathcal {A}^\mathrm {et}_n(F) , generalizing and simplifying a construction of Howe (1977). Together, these maps give a canonical bijection of G n e t ( F ) \mathcal {G}^\mathrm {et}_n(F) with A n e t ( F ) \mathcal {A}^\mathrm {et}_n(F) . We show that one obtains the Langlands correspondence by composing the map P n ( F ) → A n e <mi...
- Open AccessFunctorial products for $GL_2\times GL_3$ and the symmetric cube for $GL_2$In this paper we prove two new cases of Langlands functoriality. The first is a functorial product for cusp forms on $GL_2\times GL_3$ as automorphic forms on $GL_6$, from which we obtain our second case, the long awaited functorial symmetric cube map for cusp forms on $GL_2$. We prove these by applying a recent version of converse theorems of Cogdell and Piatetski-Shapiro to analytic properties of certain $L$-functions obtained from the method of Eisenstein series (Langlands-Shahidi method). As a consequence, we prove the bound 5/34 for Hecke eigenvalues of Maass forms over any number field and at every place, finite or infinite, breaking the crucial bound 1/6 (see below and Section 7 and 8) towards Ramanujan-Petersson and Selberg conjectures for $GL_2$. Many other applications are obtained.Open AccessFunctorial products for $GL_2\times GL_3$ and the symmetric cube for $GL_2$In this paper we prove two new cases of Langlands functoriality. The first is a functorial product for cusp forms on $GL_2\times GL_3$ as automorphic forms on $GL_6$, from which we obtain our second case, the long awaited functorial symmetric cube map for cusp forms on $GL_2$. We prove these by applying a recent version of converse theorems of Cogdell and Piatetski-Shapiro to analytic properties of certain $L$-functions obtained from the method of Eisenstein series (Langlands-Shahidi method). As a consequence, we prove the bound 5/34 for Hecke eigenvalues of Maass forms over any number field and at every place, finite or infinite, breaking the crucial bound 1/6 (see below and Section 7 and 8) towards Ramanujan-Petersson and Selberg conjectures for $GL_2$. Many other applications are obtained.
- 1 May 2004
- Published by Springer Nature in manuscripta mathematica
- Vol. 114 (1) , 1-7
Local Jacquet-Langlands correspondence and parametric degrees
- 1 May 2004
- Published by Springer Nature in manuscripta mathematica
- Vol. 114 (1) , 1-7
Local Jacquet-Langlands correspondence and parametric degrees
- 26 September 2003
- Published by Wiley in Proceedings of the London Mathematical Society
- Vol. 87 (02) , 337-362
Local Tame Lifting for GL(n) IV: Simple Characters and Base Change
- 26 September 2003
- Published by Wiley in Proceedings of the London Mathematical Society
- Vol. 87 (02) , 337-362
Local Tame Lifting for GL(n) IV: Simple Characters and Base Change
- 31 March 2003
- Published by Elsevier in Journal of Number Theory
- Vol. 99 (1) , 74-89
Explicit unramified base change: GL(p) of a p-adic field
- 31 March 2003
- Published by Elsevier in Journal of Number Theory
- Vol. 99 (1) , 74-89
Explicit unramified base change: GL(p) of a p-adic field
- 1 April 2001
- Published by Wiley in Journal of the London Mathematical Society
- Vol. 63 (2) , 364-386
Representations of Reductive p -Adic Groups: Localization of Hecke Algebras and Applications
Let F be a non-Archimedean local field and G be the group of F-points of a connected reductive group defined over F. Let M be an F-Levi subgroup of G and P = MN be a parabolic subgroup with Levi deco...
- 1 April 2001
- Published by Wiley in Journal of the London Mathematical Society
- Vol. 63 (2) , 364-386
Representations of Reductive p -Adic Groups: Localization of Hecke Algebras and Applications
Let F be a non-Archimedean local field and G be the group of F-points of a connected reductive group defined over F. Let M be an F-Levi subgroup of G and P = MN be a parabolic subgroup with Levi deco...
- 1 August 2000
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 123 (1) , 89-115
Calculs de facteurs epsilon de paires sur un corps local, II
Let F a locally compact non-Archimedean field, of residue characteristic p , and ψ a nontrivial additive character of F . Let σ, σ′ be irreducible representations of the absolute Weil group of F , each of degree a power of p and not induced from a nontrivial unramified extension of F . We give a formula for the value at $s=½ of the ϵ-factor ϵ (σ ⊗ σ ',ψ,s)$ , modulo roots of unity in ${\Bbb C}$ of order a power of p . Via the Langlands correspondence, we get an analogous formula for supercuspidal representations of ${\rm GL}_n(F)$ .- 1 August 2000
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 123 (1) , 89-115
Calculs de facteurs epsilon de paires sur un corps local, II
Let F a locally compact non-Archimedean field, of residue characteristic p , and ψ a nontrivial additive character of F . Let σ, σ′ be irreducible representations of the absolute Weil group of F , each of degree a power of p and not induced from a nontrivial unramified extension of F . We give a formula for the value at $s=½ of the ϵ-factor ϵ (σ ⊗ σ ',ψ,s)$ , modulo roots of unity in ${\Bbb C}$ of order a power of p . Via the Langlands correspondence, we get an analogous formula for supercuspidal representations of ${\rm GL}_n(F)$ .- 1 June 2000
- Published by Springer Nature in manuscripta mathematica
- Vol. 102 (2) , 211-225
Correspondance de Jacquet-Langlands explicite
- 1 June 2000
- Published by Springer Nature in manuscripta mathematica
- Vol. 102 (2) , 211-225
Correspondance de Jacquet-Langlands explicite
- 1 October 1999
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 119 (1) , 53-97
Semisimple Types in GLn
This paper is concerned with the smooth representation theory of the general linear group G=GL(F) of a non-Archimedean local field F. The point is the (explicit) construction of a special series of irreducible representations of compact open subgroups, called semisimple types, and the computation of their Hecke algebras. A given semisimple type determines a Bernstein component of the category of smooth representations of G; that component is then the module category for a tensor product of affine Hecke algebras; every component arises this way. Moreover, all Jacquet functors and parabolic induction functors connecting G with its Levi subgroups are described in terms of standard maps between affine Hecke algebras. These properties of semisimple types depend on their special intertwining properties which in turn imply strong bounds on the support of coefficient functions.
- 1 October 1999
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 119 (1) , 53-97
Semisimple Types in GLn
This paper is concerned with the smooth representation theory of the general linear group G=GL(F) of a non-Archimedean local field F. The point is the (explicit) construction of a special series of irreducible representations of compact open subgroups, called semisimple types, and the computation of their Hecke algebras. A given semisimple type determines a Bernstein component of the category of smooth representations of G; that component is then the module category for a tensor product of affine Hecke algebras; every component arises this way. Moreover, all Jacquet functors and parabolic induction functors connecting G with its Levi subgroups are described in terms of standard maps between affine Hecke algebras. These properties of semisimple types depend on their special intertwining properties which in turn imply strong bounds on the support of coefficient functions.