王子放置与有限辛群最大单位子群的共伴随轨道
Rook placements and coadjoint orbits for maximal unipotent subgroups of finite symplectic groups
AI总结：
本文研究了有限辛群最大单位子群的共伴随轨道与正交王子放置的关系，并给出了最大维度轨道特征标的显式公式。
摘要：
设U是有限域上辛群的最大单位子群。根据Kirillov的轨道方法，群U的共伴随轨道在描述U的不可约复特征标中起关键作用。几乎所有重要的轨道和特征标类别到目前为止都可以统一描述为与所谓的正交王子放置相关的轨道和特征标。在本文中，我们按照Mackey小群方法的精神，为相应的不可约特征标构造半直接分解。作为推论，我们给出了对应于最大可能维度轨道的特征标的显式公式。
英文摘要：
Let $U$ be a maximal unipotent subgroup in a symplectic group over a finite field of sufficiently large characteristic $p$. According to the Kirillov's orbit method, the coadjoint orbits of the group $U$ play the key role in the description of irreducible complex characters of $U$. Almost all important classes of orbits and characters studied to the moment can be uniformly described as the orbits and characters associated with so-called orthogonal rook placements. In the paper, we construct a semi-direct decomposition for the corresponding irreducible characters in the spirit of the Mackey little group method. As a corollary, we present an explicit formula for the character corresponding to an orbit of maximal possible dimension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
