The structure of integral parabolic subgroups of orthogonal groups (Q2186024)

In the present paper, the author studies the structure of parabolic subgroups of orthogonal groups over \(\mathbb{Z}\). In the orthogonal case, the symmetric space is Hermitian only if the signature of a non-degenerate quadratic space \(V\) over \(\mathbb{R}\) is \((n, 2)\), where there are at most two types of maximal parabolic subgroups, because the dimension of a rational isotropic subspace can be at most \(2\) in this case. The author gives the precise form of canonical boundary components in toroidal compactifications of these orthogonal Shimura varieties. In particular, this boundary component is a finite quotient of a Kuga-Sato variety.