Matrix coefficients and Iwahori-Hecke algebra modules

Ben Brubaker; Daniel Bump; Solomon Friedberg

doi:10.1016/j.aim.2016.05.012

Matrix coefficients and Iwahori-Hecke algebra modules

Ben Brubaker, Daniel Bump, Solomon Friedberg

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of the image of spherical and Iwahori-fixed vectors in the unramified principal series for this class of models. We provide an explicit alternator expression for the image of spherical vectors under these functionals in terms of the representation theory of the dual group.

Original language	English (US)
Pages (from-to)	247-271
Number of pages	25
Journal	Advances in Mathematics
Volume	299
DOIs	https://doi.org/10.1016/j.aim.2016.05.012
State	Published - Aug 20 2016

Bibliographical note

Funding Information:
This work was supported by NSF grants DMS-1406238 (Brubaker), DMS-1001079 (Bump), and DMS-1500977 (Friedberg) and NSA grant H98230-13-1-0246 (Friedberg).

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Bessel functional
Casselman-Shalika formula
Hecke algebra
Unique functional
Universal principal series

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title = "Matrix coefficients and Iwahori-Hecke algebra modules",

abstract = "We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of the image of spherical and Iwahori-fixed vectors in the unramified principal series for this class of models. We provide an explicit alternator expression for the image of spherical vectors under these functionals in terms of the representation theory of the dual group.",

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AU - Bump, Daniel

AU - Friedberg, Solomon

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N2 - We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of the image of spherical and Iwahori-fixed vectors in the unramified principal series for this class of models. We provide an explicit alternator expression for the image of spherical vectors under these functionals in terms of the representation theory of the dual group.

AB - We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of the image of spherical and Iwahori-fixed vectors in the unramified principal series for this class of models. We provide an explicit alternator expression for the image of spherical vectors under these functionals in terms of the representation theory of the dual group.

KW - Bessel functional

KW - Casselman-Shalika formula

KW - Hecke algebra

KW - Unique functional

KW - Universal principal series

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SP - 247

EP - 271

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Matrix coefficients and Iwahori-Hecke algebra modules

Abstract

Bibliographical note

Keywords

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