The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups

Nadya Gurevich; Edmund Karasiewicz

doi:10.1093/imrn/rnab346

The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups

Nadya Gurevich, Edmund Karasiewicz

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform. This method provides a conceptual explanation of the appearance of characters of a dual group in the Casselman-Shalika formula.

Original language	American English
Pages (from-to)	11148-11179
Number of pages	32
Journal	International Mathematics Research Notices
Volume	2022
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnab346
State	Published - 21 Dec 2021

Keywords

Mathematics - Number Theory
Mathematics - Representation Theory

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1093/imrn/rnab346

Cite this

@article{61ba947587c84c11b63c83b5cab23077,

title = "The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups",

abstract = "We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform. This method provides a conceptual explanation of the appearance of characters of a dual group in the Casselman-Shalika formula.",

keywords = "Mathematics - Number Theory, Mathematics - Representation Theory",

author = "Nadya Gurevich and Edmund Karasiewicz",

year = "2021",

month = dec,

day = "21",

doi = "10.1093/imrn/rnab346",

language = "American English",

volume = "2022",

pages = "11148--11179",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "14",

}

TY - JOUR

T1 - The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups

AU - Gurevich, Nadya

AU - Karasiewicz, Edmund

PY - 2021/12/21

Y1 - 2021/12/21

N2 - We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform. This method provides a conceptual explanation of the appearance of characters of a dual group in the Casselman-Shalika formula.

AB - We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform. This method provides a conceptual explanation of the appearance of characters of a dual group in the Casselman-Shalika formula.

KW - Mathematics - Number Theory

KW - Mathematics - Representation Theory

UR - http://www.scopus.com/inward/record.url?scp=85134578829&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnab346

DO - 10.1093/imrn/rnab346

M3 - Article

SN - 1073-7928

VL - 2022

SP - 11148

EP - 11179

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 14

ER -

The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this