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arXiv · 2607.12522

M\"obius functions for pseudo-Levi subgroups in finite general linear and symplectic groups

Aritra Kundu
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Abstract

In this paper, we compute the M\"obius function on the set 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 $q$. The M\"obius 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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Aritra Kundu. 2026-07-14. M\"obius functions for pseudo-Levi subgroups in finite general linear and symplectic groups. https://arxiv.org/abs/2607.12522

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