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Basic functions and unramified local L-factors for split groups
Li, Wen-Wei1,2
AbstractAccording 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.
KeywordL-function Satake isomorphism generalized Kostka-Foulkes polynomial
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000400086700002
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Document Type期刊论文
Corresponding AuthorLi, Wen-Wei
Affiliation1.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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