A Galois-equivariant Dade-Glauberman-Nagao correspondence with central defect
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 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.
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BibTeX
@misc{chen2026galoisequivariant,
title = {{A Galois-equivariant Dade-Glauberman-Nagao correspondence with central defect}},
author = {Shi Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37558},
eprint = {2609.37558},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37558},
}
RIS
TY - UNPB
TI - A Galois-equivariant Dade-Glauberman-Nagao correspondence with central defect
AU - Shi Chen
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37558
UR - https://arxiv.org/abs/2609.37558
AB - 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 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.
ER -