有限正交群的Sylow $p$-子群中与车放置相关的轨道和特征标
Orbits and characters associated with rook placements for Sylow $p$-subgroups of finite orthogonal groups
AI总结：
本文研究有限正交群Sylow p-子群中与正交车放置相关的余伴随轨道，构造极化并给出不可约特征的半直积分解，进而计算轨道维数。
摘要：
设 $U$ 是特征为 $p$ 的有限域上经典群的一个 Sylow $p$-子群。群 $U$ 的余伴随轨道在描述 $U$ 的不可约复特征标中起着关键作用。迄今为止研究过的几乎所有重要的轨道和特征标类都可以统一描述为与所谓的正交车放置相关的轨道和特征标。在本文中，我们研究正交群的此类轨道。我们为这样的轨道上的典范形式构造了一个极化，并按照 Mackey 小群方法的精神，给出了相应不可约特征的半直积分解。作为推论，我们计算了与正交车放置相关的轨道的维数。
英文摘要：
Let $U$ be a Sylow $p$-subgroup in a classical group over a finite field of characteristic $p$. 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 study such orbits for the orthogonal group. We construct a polarization for the canonical form on such an orbit and present a semi-direct decomposition for the corresponding irreducible characters in the spirit of the Mackey little group method. As a corollary, we compute the dimension of an orbit associated with an orthogonal rook placement.
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。
