2021/06/02 by Mikhail Ignatev, Ignatev, Mikhail, Ivan Penkov +1
Mathematics · #14J50 #14L30 #14M15 #14M17 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2106.00989
openalex publication_date 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We compute the group of automorphisms of an arbitrary ind-variety of (possibly isotropic) generalized flags. Such an ind-variety is a homogeneous ind-space for one of the ind-groups SL(∞), O(∞) or Sp(∞). We show that the respective automorphism groups are much larger than SL(∞), O(∞) or Sp(∞), and present the answer in terms of Mackey groups. The latter are groups of automorphisms of nondegenerate pairings of (in general infinite-dimensional) vector spaces. An explicit matrix form of the automorphism group of an arbitrary ind-variety of generalized flags is also given. The case of the Sato grassmannian is considered in detail, and its automorphism group is the projectivization of the connected component of unity in the group Japanese GL(∞).