The extension of the terminology "flag variety" is reasonable, because points of "G"/"P" can still be described using flags. When "G" is a classical group, such as a symplectic group or orthogonal group, this is particularly transparent. If ("V", "ω") is a symplectic vector space then a partial flag in "V" is "isotropic" if the symplectic form vanishes on proper subspaces of "V" in the flag. The stabilizer of an isotropic flag is a parabolic subgroup of the symplectic group Sp("V","ω"). For orthogonal groups there is a similar picture, with a couple of complications. First, if F is not algebraically closed, then isotropic subspaces may not exist: for a general theory, one needs to use the split orthogonal groups. Second, for vector spaces of even dimension 2"m", isotropic subspaces of dimension "m" come in two flavours ("self-dual" and "anti-self-dual") and one needs to distinguish these to obtain a homogeneous space.