有限典型群的Sylow p-子群的极大与次极大维轨道
Orbits of maximal and submaximal dimension for Sylow $p$-subgroups of finite classical groups
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中文总结 AI 辅助
本文对有限典型群的Sylow p-子群的辛群预极大维轨道与正交群极大维轨道分类，计算其轨道数，发现该数为q-1的非负整系数多项式，验证了Isaacs猜想。
中文摘要 AI 辅助
设U是有限域上特征为p且q足够大的典型群中的一个Sylow p-子群，群U的余伴随轨道在描述U的不可约复特征时起关键作用。本文中，我们对辛群的这类预极大维轨道以及正交群的这类极大维轨道进行分类，作为推论，我们计算了上述所有轨道的数量。结果表明，每个这样的数量都是q-1的整系数非负多项式，这与Isaacs猜想一致。
英文摘要
Let $U$ be a Sylow $p$-subgroup in a classical group over a finite field with $q$ elements of characteristic $p$ large enough. The coadjoint orbits of the group $U$ play the key role in the description of irreducible complex characters of $U$. In the paper, we provide a classification of such orbits of pre-maximal dimension for symplectic groups and orbits of maximal dimension for orthogonal groups. As a corollary, we compute the number of all orbits mentioned above. It turned out that each of these numbers is a polynomial in $q - 1$ with integer non-negative coefficients, which agrees with the Isaacs' conjecture.
