Basic functions and unramified local L-factors for split groups
Basic functions and unramified local L-factors for split groups
复制标题
分组的基本函数和未分支的局部 L 因子
DOI：
10.1007/s11425-015-0730-4
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Wen
中科院分区：
文献类型：
--
作者：
Wen
根据Braverman， Kazhdan和Ngô的一个程序，对于一大类分裂的未分枝化约群G和对偶群Ĝ的表示ρ，当Re(s) < 0 >时，未分枝化局部L因子L（s, π, ρ）可以表示为非紧支持函数fρ，s的π(fρ,s)的迹。这样的函数应该在几何或组合学方面有有用的解释，并且可以将其插入迹公式中以研究自同构l函数的某些和。由于Sakellaridis创造了“基本函数”一词，它也符合关于约化一元群的Schwartz空间的猜想框架；这应该会导致（G, ρ）的一般化tamagawa - godemi - jacquet理论。本文导出了基本函数fρ，s的一些基本性质，并用不变理论解释了这些性质。特别地，它们的系数被解释为由Panyushev定义的某些广义Kostka-Foulkes多项式。这些系数可以被编码成有理生成函数。
According to a program of Braverman, Kazhdan and Ngô, for a large class of split unramified reductive groups G and representations ρ of the dual group Ĝ, the unramified local L-factor L(s, π, ρ) can be expressed as the trace of π(fρ,s) for a function fρ,s with non-compact support whenever Re(s) ≫ 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, ρ). In this paper, we derive some basic properties for the basic functions fρ,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.
影响因子：
4.9
作者：
T. Finis;E. Lapid;W. Müller
通讯作者：
W. Müller