论文标题
部分可观测时空混沌系统的无模型预测
Generic Hecke algebra and theta correspondence over finite fields
论文作者
论文摘要
我们研究了由有限领域的I型双对的某些Harish-Chandra系列之间的theta对应关系引起的Hecke代数模块。对于正在考虑的Hecke代数的乘积，我们表明有一个通用的Hecke代数模块，其Prime Powers的专业化为Hecke代数模块提供了明确描述的Hecke代数模块。作为应用程序，我们证明了所有不可约表示的首次出现指数的保护关系。作为另一个应用程序，我们将Aubert-Michel-Rouquier的结果概括为Harish-Chandra系列之间的Theta对应关系。
We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for type I dual pairs over finite fields. For the product of the pair of Hecke algebras under consideration, we show that there is a generic Hecke algebra module whose specializations at prime powers give the Hecke algebra modules and whose specialization at $1$ can be explicitly described. As an application, we prove the conservation relation on the first occurrence indices for all irreducible representations. As another application, we generalize the results of Aubert-Michel-Rouquier and Pan on theta correspondence between the Harish-Chandra series.
