---
date: 2022-04-24 19:42
modification date: Sunday 24th April 2022 19:42:57
title: "affine Grassmannian"
aliases: [affine Grassmannian]
created: 2023-07-11T14:05
updated: 2023-07-11T14:07
---

Last modified date: <%+ tp.file.last_modified_date() %>

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [Cartan decomposition](Cartan%20decomposition)
	- [spherical Hecke algebra](spherical%20Hecke%20algebra)

---

# affine Grassmannian

![](2023-07-11.png)

Another way of describing this is as the group of formal loops in $G$ modulo the subgroup of formal arcs, i.e. formal loops that one can "fill in" to formal discs.

![](attachments/Pasted%20image%2020220424194259.png)
![](attachments/Pasted%20image%2020220424194352.png)