Rank-2 Vector Bundles on ind-Grassmannians

An ind-Grassmannian X = lim→ G(k i ; V n i ) is linear if almost all defining embeddings ϕ m : G(k m ; V n m )→G(k m + 1; V n m + 1) are of degree 1, and is twisted if infinitely many defining embeddings ϕ m are of degree higher than 1. In this paper we give a complete description of finite-rank vector bundles on any linear ind-Grassmannian, and prove that any vector bundle of rank 2 on a twisted ind-Grassmannian is trivial. Our work extends work by W. Barth, J. Donin, I. Penkov, E. Sato, A. Tyurin