AI 中文总结
本文针对特征p足够大的有限域上典型正交群的Sylow p-子群，对其预极大维余伴随轨道分类，计算轨道数并验证其符合Isaacs猜想。
AI 中文摘要
设U是有限域上特征为p、q元的典型正交群中的Sylow p-子群，特征p足够大。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。本文对这类预极大维轨道进行分类，作为推论计算上述所有轨道的数量，结果表明每个数量都是q-1的非负整数系数多项式，这与Isaacs猜想相符。
英文摘要
Let $U$ be a Sylow $p$-subgroup in a classical orthogonal 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. 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.
Comments16 pages
