Möbius functions for pseudo-Levi subgroups in finite general linear and symplectic groups
Abstract
In this paper, we compute the Möbius function on the poset of pseudo-Levi subgroups containing a fixed maximal torus of two families of finite groups, GLn(q) and Sp2n(q), for some natural number n and a prime power q, where q>2n+1. For the general linear group, we consider arbitrary tori, but for symplectic groups, we restrict to tori corresponding to the bipartitions of n into odd integers. Also, we assume q is even for the case of symplectic groups. The Möbius function for the set of pseudo-Levi subgroups of a finite group G is important for an explicit evaluation of the formula expressing the decomposition of tensor products of characters, as proved in Theorem 2 of the paper ''Multiplicity of characters of finite reductive groups and Drinfeld doubles'' [arXiv:2512.01432].
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BibTeX
@misc{kundu2026möbius,
title = {{Möbius functions for pseudo-Levi subgroups in finite general linear and symplectic groups}},
author = {Aritra Kundu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.12522},
eprint = {2607.12522},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12522},
}
RIS
TY - UNPB
TI - Möbius functions for pseudo-Levi subgroups in finite general linear and symplectic groups
AU - Aritra Kundu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2607.12522
UR - https://arxiv.org/abs/2607.12522
AB - In this paper, we compute the Möbius function on the poset of pseudo-Levi subgroups containing a fixed maximal torus of two families of finite groups, GL_n(q) and Sp_2n(q), for some natural number n and a prime power q, where q>2n+1. For the general linear group, we consider arbitrary tori, but for symplectic groups, we restrict to tori corresponding to the bipartitions of n into odd integers. Also, we assume q is even for the case of symplectic groups. The Möbius function for the set of pseudo-Levi subgroups of a finite group G is important for an explicit evaluation of the formula expressing the decomposition of tensor products of characters, as proved in Theorem 2 of the paper ''Multiplicity of characters of finite reductive groups and Drinfeld doubles'' [arXiv:2512.01432].
ER -