Transfer operators and Hankel transforms between relative trace formulas, I: Character theory
Transfer operators and Hankel transforms between relative trace formulas, I: Character theory
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相对迹公式之间的传递算子和 Hankel 变换，I：特征理论
DOI：
10.1016/j.aim.2021.108010
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发表时间：
2022
影响因子：
1.7
通讯作者：
Sakellaridis, Yiannis
中科院分区：
文献类型：
--
作者：
Sakellaridis, Yiannis
朗兰兹函性猜想，在“超越内窥镜”计划中重新表述，预测了不同群G1，G2的（稳定）迹公式之间的比较，对于它们的L-群之间的每个态射G1 L→ LG 2。这个猜想可以被看作是一个更一般的猜想的特例，它用球面簇代替了约化群，用它的推广，相对迹公式代替了迹公式。本文及其续篇[21]的目的是通过示例证明相对迹公式之间存在“转移算子”，其推广了内窥镜检查的标量转移因子。这些转移算子具有所有的性质，人们可以期望从一个跟踪公式比较：匹配，基本引理的赫克代数，转移（相对）字符。最重要的是，令人惊讶的是，他们似乎是阿贝尔性质（至少，在本文考虑的低秩的例子），即使他们包括函关系的非阿贝尔调和分析。因此，他们是服从泊松求和公式的应用，以执行全球比较。此外，我们表明，这些阿贝尔变换有一定的结构，目前逃脱我们的理解，在其整体变形的良好理解的运营商时，所考虑的空间被替换为他们的“渐近锥”。本文研究了SL 2的Kuznetsov公式和稳定迹公式及其退化（以及PGL 2中环面周期的相对迹公式）的（相对）性质，并证明了它们在显式转移算子下是如何相互对应的
The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between the (stable) trace formulas of different groups G 1, G 2 for every morphism G 1 L→ L G 2 between their L-groups. This conjecture can be seen as a special case of a more general conjecture, which replaces reductive groups by spherical varieties and the trace formula by its generalization, the relative trace formula. The goal of this article and its continuation [21] is to demonstrate, by example, the existence of “transfer operators” between relative trace formulas, which generalize the scalar transfer factors of endoscopy. These transfer operators have all properties that one could expect from a trace formula comparison: matching, fundamental lemma for the Hecke algebra, transfer of (relative) characters. Most importantly, and quite surprisingly, they appear to be of abelian nature (at least, in the low-rank examples considered in this paper), even though they encompass functoriality relations of non-abelian harmonic analysis. Thus, they are amenable to application of the Poisson summation formula in order to perform the global comparison. Moreover, we show that these abelian transforms have some structure—which presently escapes our understanding in its entirety—as deformations of well-understood operators when the spaces under consideration are replaced by their “asymptotic cones”. In this first paper we study (relative) characters for the Kuznetsov formula and the stable trace formula for SL 2 and their degenerations (as well as for the relative trace formula for torus periods in PGL 2), and we show how they correspond to each other under explicit transfer operators.
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Satake 逆变换
DOI：
10.1007/978-3-319-94833-1_11
发表时间：
2014
期刊：
arXiv: Representation Theory
影响因子：
--
作者：
Y. Sakellaridis
通讯作者：
Y. Sakellaridis
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影响因子：
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作者：
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影响因子：
0.5
作者：
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通讯作者：
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影响因子：
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作者：
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通讯作者：
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影响因子：
1
作者：
N. Chau
通讯作者：
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