Möbius functions for pseudo-Levi subgroups in finite general linear and symplectic groups
arXiv:2607.12522
The paper calculates the Möbius function for the lattice of pseudo‑Levi subgroups that contain a fixed maximal torus in the finite groups GLₙ(q) and Sp₂ₙ(q), providing data needed for explicit character tensor‑product decompositions.
Abstract
In this paper, we compute the Möbius function on the set of pseudo-Levi subgroups containing a fixed maximal torus of two families of finite groups, and , for some natural number and a prime power . The Möbius function for the set of pseudo-Levi subgroups of a finite group 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].