On the Geometry of the Flag Varieties of Orthogonal group and Symplectic group

Abstract

The aim of this paper is to discuss an important discourse, as most literatures highlighted the dimension of partial flag in a certain manner, according to a fixed definition that does not include all possible cases. In the present paper the existence of two different cases of flags in the partial flag varieties of the groups and is explained wholly. In addition to this we will proceed by calculating the dimensions for all the given cases after pertaining the signature of these flags that are studied.