2019/10/26 by Alexander S. Tikhomirov, Tikhomirov, A., Ivan Penkov +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1910.12005
openalex publication_date 2019/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(∞) (respectively, O(∞) or Sp(∞) for isotropic generalized flags), and the current paper constructs them in purely algebraic-geometric terms