Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Starčič, Tadej
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220681530