 In the unpolarized case, define the "monodromy group" Γ to be the subgroup of GL("Hk"("X"0, Z)) consisting of all automorphisms induced by a homotopy class of curves in "B" as above.The flag variety is a quotient of a Lie group by a parabolic subgroup, and the monodromy group is an arithmetic subgroup of the Lie group.The global unpolarized period domain is the quotient of the local unpolarized period domain by the action of Γ (it is thus a collection of double cosets).