Isotropy groups of the action of orthogonal similarity on skew-symmetric and on complex orthogonal matrices

2025/12/16 by Starčič, Tadej
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.14871

Abstract

We compute and analyze isotropy subgroups of the complex orthogonal group with respect to the similarity transformation on itself and on skew-symmetric matrices. Their group structure is related to a group of certain nonsingular block matrices whose blocks are rectangular block Toeplitz.

Citations

• Isotropy groups of the action of orthogonal *congruence on Hermitian matrices
• Isotropy groups of the action of orthogonal similarity on symmetric matrices

Related

• Isotropy groups of the action of orthogonal similarity on symmetric matrices
• Isotropy groups of the action of orthogonal *congruence on Hermitian matrices
• The stabilizers for the action of orthogonal similarity on symmetric matrices and orthogonal *-conjugacy on Hermitian matrices
• On isometry groups of self-adjoint traceless and skew-symmetric matrices
• Factorization of Symmetric Matrices and Actions on Σ_k