On the intersection of local Arthur packets for classical groups and applications
On the intersection of local Arthur packets for classical groups and applications
复制标题
关于经典组和应用程序的本地 Arthur 数据包的交集
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Chi
中科院分区：
文献类型：
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作者：
Alexander Hazeltine;Baiying Liu;Chi
本文对辛的和分裂的奇特殊正交群，给出了局部亚瑟包的交问题的理论。具体地说，根据Atobe对M{\oe}glin构造局部亚瑟分组的重新表述，我们给出了构造数据上的一组完整的算子，在此基础上，我们给出了判定给定表示是否为亚瑟类型的算法和Sage码.此外，对于任何亚瑟类型的表示$\pi$，我们给出了集合$ \Psi（\pi）=\{ \text{local亚瑟parameter }\psi \的精确公式。|\ \text{本地亚瑟数据包} \Pi_{\psi} \text{ contains } \pi\}.$$我们的结果有许多应用，包括精确计数任何局部亚瑟包中的调和表示，指定和表征$\pi$中的局部亚瑟参数，特别是当$\pi$属于几个局部亚瑟包但不属于任何局部亚瑟包时.
In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on M{\oe}glin's construction of local Arthur packets, we give a complete set of operators on the construction data, based on which, we provide algorithms and Sage codes to determine whether a given representation is of Arthur type. Furthermore, for any representation $\pi$ of Arthur type, we give a precise formula for the set $$ \Psi(\pi)=\{ \text{local Arthur parameter }\psi \ | \ \text{the local Arthur packet } \Pi_{\psi} \text{ contains } \pi\}.$$ Our results have many applications, including the precise counting of tempered representations in any local Arthur packet, specifying and characterizing"the"local Arthur parameter in $\Psi(\pi)$ for $\pi$, especially when $\pi$ belongs to several local Arthur packets but does not belong to any local $L$-packet of Arthur type.