Year: 2026
Type: preprint
Abstract: We construct a correspondence between ordinary irreducible characters of height zero above the generalized Dade-Glauberman-Nagao correspondence for blocks with central defect. The correspondence is equivariant under group and Galois automorphisms and satisfies a block relation between $\mathcal{H}$-triples. For each pair of corresponding characters, one pair of associated projective representations realizes matching factor sets, equal central scalars, synchronized mixed comparison functions and compatible block correspondences for every intermediate group. The construction uses the multiplicity algebra over the group algebra of the central defect subgroup, a normalized integral lift of a residual semilinear realization, and a graded corner isomorphism. It treats all central-character fibers, including those with nontrivial central character. We also obtain a form suited to normal $p$-sections in an Alperin-McKay-Navarro reduction.
Source: arXiv (Cornell University)
Author: Chen, Shi
Institution: Central China Normal University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214939509