According to wikipedia,
the affine Grassmannian of an algebraic group over a field is an ind-scheme which can be thought of as a flag variety for the loop group
The affine Grassmannian is ind-representable. Affine Grassmannian of admits embedding into Sato Grassmanian.
(Definition 1.1.1 of #Zhu2016) Let be a field and let be a -algebra. An -family of lattices in is a finitely generated projective submodule of such that .
(Definition 1.1.2 of #Zhu2016) The affine Grassmannian for is the presheaf that assigns to every -algebra the set of -families of lattices in .
(Section 1.2 of #Zhu2016) Let be a field and let be an affine -group. If is a -algebra, let and let . Let be the trivial -torsor over .
The affine Grassmannian of is the presheaf that assigns to every -algebra the set of pairs , where is a -torsor on and is a trivialization.
Evgeny Feigin, Michael Finkelberg, Markus Reineke, Degenerate affine Grassmannians and loop quivers, http://arxiv.org/abs/1410.0777
Xinwen Zhu, An introduction to affine Grassmannians and the geometric Satake equivalence, arXiv:1603.05593.
Bhargav Bhatt, Peter Scholze, Projectivity of the Witt vector affine Grassmannian, Invent. math. 209, 329-423 (2017) doi arXiv:1507.06490
Alexander Schmitt, Affine flag manifolds and principal bundles, Trends in Mathematics, Springer 2010
Last revised on August 15, 2023 at 20:23:02. See the history of this page for a list of all contributions to it.