Whittaker-Shintani functions for general linear groups over \(p\)-adic fields
type: Item
instance of: scholarly article
title: Whittaker-Shintani functions for general linear groups over \(p\)-adic fields
zbMATH Open document ID: 1406.22021
author: Lei Zhang
published in: Science China. Mathematics
publication date: 2018-03-16T00:00:00Z
review text: As announced in his joint work with \textit{D. Jiang} and \textit{L. Zhang} [Geom. Funct. Anal. 24, No. 2, 552--609 (2014; Zbl 1298.11046); \textit{L. Zhang}, Manuscr. Math. 148, No. 1--2, 213--233 (2015; Zbl 1327.22022)] on calculating local zeta integrals, the author gives an explicit formula for the Whittaker-Shintani function (associated to a pair of unramified characters) for a general linear group over a p-adic field. He also provides a relation between Whittaker-Shintani functions and local Bessel models. As the author indicates, his result is largely based on the work of Kato-Murase-Sugano for orthogonal groups [\textit{S.-i. Kato} et al., Tohoku Math. J. (2) 55, No. 1, 1--64 (2003; Zbl 1037.22034)]. There are also analogous results for symplectic groups, by \textit{A. Murase} and \textit{T. Sugano} [Compos. Math. 79, No. 3, 321--349 (1991; Zbl 0731.11026)] and \textit{X. Shen} [Int. Math. Res. Not. 2014, No. 21, 5769--5831 (2014; Zbl 1306.22009)].
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F85
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 6850824
zbMATH Keywords: Bessel models
zbMATH Keywords: local factors
zbMATH Keywords: Whittaker-Shintani functions
reviewed by: Kam-Fai Tam
MaRDI profile type: Publication
full work available at URL: s11425-016-9064-6
OpenAlex ID: W2746142308
cites work: Multiplicity one theorems
cites work: A corollary to Bernstein's theorem and Whittaker functionals on the metaplectic group
cites work: Q3926802
cites work: Q3009492
cites work: Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
cites work: Uniqueness of Bessel models: the archimedean case
cites work: A product of tensor product \(L\)-functions of quasi-split classical groups of Hermitian type
cites work: Multiplicity one theorems: the Archimedean case
cites work: Whittaker-Shintani function for orthogonal groups
cites work: Q3356365
cites work: Shintani functions and automorphic \(L\)-functions for \(GL(n)\)
cites work: On the unramified spectrum of spherical varieties over p-adic fields
cites work: The Whittaker–Shintani Functions for Symplectic Groups
DOI: 10.1007/S11425-016-9064-6
description: scientific article; zbMATH DE number 6850824