  We define the class of admissible linear embeddings of flag varieties. The
definition is given in the general language of algebraic geometry. We then
prove that an admissible linear embedding of flag varieties has a certain
explicit form in terms of linear algebra. This result enables us to show that
any direct limit of admissible embeddings of flag varieties is isomorphic to an
ind-variety of generalized flags as defined in [DP]. These latter ind-varieties
have been introduced in terms of the ind-group SL(\infty) (respectively,
O(\infty) or Sp(\infty) for isotropic generalized flags), and the current paper
constructs them in purely algebraic-geometric terms

Algebraic Geometry