论文标题
关于古典组和应用的本地亚瑟数据包的交集
On the intersection of local Arthur packets for classical groups and applications
论文作者
论文摘要
在本文中，对于符合和奇特的特殊正交群体，我们对局部Arthur数据包相交问题的理论进行了描述。具体来说，随着Atobe对M– Glin的本地Arthur数据包的重新制定，我们为构造数据提供了完整的操作员，我们提供了算法和SAGE代码，以确定给定表示的代表是否为Arthur类型。此外，对于Arthur类型的任何表示$π$，我们为SET $$ψ（π）= \ {\ text {local arthur parameter}ψ\ |提供精确的公式。 \ \ text {local arthur packet}π_ψ\ text {contains}π\}。$$ 我们的结果有许多应用程序，包括在任何本地Arthur数据包中进行钢化表示的精确计数，并表征和表征“ $π$的$ψ（π）$中的本地Arthur参数，尤其是当$π$属于几个本地Arthur Packet，但不属于Arthur of Arthur of Arthur of Arthur类型的任何本地Arthur Packet。
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 Mœglin'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 $π$ of Arthur type, we give a precise formula for the set $$ Ψ(π)=\{ \text{local Arthur parameter }ψ\ | \ \text{the local Arthur packet } Π_ψ \text{ contains } π\}.$$ 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 $Ψ(π)$ for $π$, especially when $π$ belongs to several local Arthur packets but does not belong to any local $L$-packet of Arthur type.
