Basic functions and unramified local L-factors for split groups | |
Li, Wen-Wei1,2 | |
2017-05-01 | |
Source Publication | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
Volume | 60Issue:5Pages:777-812 |
Abstract | According to a program of Braverman, Kazhdan and Ng, for a large class of split unramified reductive groups G and representations rho of the dual group Ae, the unramified local L-factor L(s, pi, rho) can be expressed as the trace of pi(f (rho,s) ) for a function f (rho,s) with non-compact support whenever Re(s) ae << 0. Such a function should have useful interpretations in terms of geometry or combinatorics, and it can be plugged into the trace formula to study certain sums of automorphic L-functions. It also fits into the conjectural framework of Schwartz spaces for reductive monoids due to Sakellaridis, who coined the term basic functions; this is supposed to lead to a generalized Tamagawa-Godement-Jacquet theory for (G, rho). In this paper, we derive some basic properties for the basic functions f (rho,s) and interpret them via invariant theory. In particular, their coefficients are interpreted as certain generalized Kostka-Foulkes polynomials defined by Panyushev. These coefficients can be encoded into a rational generating function. |
Keyword | L-function Satake isomorphism generalized Kostka-Foulkes polynomial |
DOI | 10.1007/s11425-015-0730-4 |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000400086700002 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25968 |
Collection | 数学所 |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
Recommended Citation GB/T 7714 | Li, Wen-Wei. Basic functions and unramified local L-factors for split groups[J]. SCIENCE CHINA-MATHEMATICS,2017,60(5):777-812. |
APA | Li, Wen-Wei.(2017).Basic functions and unramified local L-factors for split groups.SCIENCE CHINA-MATHEMATICS,60(5),777-812. |
MLA | Li, Wen-Wei."Basic functions and unramified local L-factors for split groups".SCIENCE CHINA-MATHEMATICS 60.5(2017):777-812. |
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