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Orbits of maximal and submaximal dimension for Sylow p-subgroups of finite classical groups
Abstract
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.
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BibTeX
@misc{ignatev2026orbits,
title = {{Orbits of maximal and submaximal dimension for Sylow $p$-subgroups of finite classical groups}},
author = {Mikhail Ignatev and Mikhail Venchakov},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27523},
eprint = {2608.27523},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27523},
}
RIS
TY - UNPB
TI - Orbits of maximal and submaximal dimension for Sylow p-subgroups of finite classical groups
AU - Mikhail Ignatev
AU - Mikhail Venchakov
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27523
UR - https://arxiv.org/abs/2608.27523
AB - 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.
ER -