PreprintCC BY 4.0arXiv
Centralizers of elements in the orthogonal, symplectic and unitary groups
Abstract
We explicitly compute and parametrize the centralizers of elements, encompassing dege\-ne\-rate and unipotent ones, in the orthogonal, symplectic, and unitary gro\-ups over the real and complex fields, including the indefinite cases. The same approach simultaneously yields the isotropy groups of H-skew-symme\-tric, Hamiltonian, and H-Hermitian matrices under the adjoint representations of the corresponding classical groups. The resulting groups are conjugate to subgroups of nonsingular block matrices whose blocks exhibit a rectangular block Toeplitz structure.
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BibTeX
@misc{starcic2026centralizers,
title = {{Centralizers of elements in the orthogonal, symplectic and unitary groups}},
author = {Tadej Starčič},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05471},
eprint = {2610.05471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05471},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Centralizers of elements in the orthogonal, symplectic and unitary groups
AU - Tadej Starčič
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05471
UR - https://arxiv.org/abs/2610.05471
AB - We explicitly compute and parametrize the centralizers of elements, encompassing dege\-ne\-rate and unipotent ones, in the orthogonal, symplectic, and unitary gro\-ups over the real and complex fields, including the indefinite cases. The same approach simultaneously yields the isotropy groups of H-skew-symme\-tric, Hamiltonian, and H-Hermitian matrices under the adjoint representations of the corresponding classical groups. The resulting groups are conjugate to subgroups of nonsingular block matrices whose blocks exhibit a rectangular block Toeplitz structure.
ER -