About two decades ago, Ivan Dimitrov and I defined ind-varieties of generalized flags. These varieties are nothing but
G/P for G=GL(infty) and a parabolic subgroup P of G. In this talk I would like to explain that the ind varieties of
generalized flags can be alternatively defined in a purely algebraic-geometric fashion as direct limits of linear
embeddings of usual flag varieties. The fact that the so-defined ind-varieties are homogeneous ind-spaces for
GL(infty) is then a consequence of the comparison theorem.
This theorem has also analogs for varieties of isotropic flags. Joint work with A. S. Tikhomirov
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5312