---
date: 2022-04-25 22:36
modification date: Monday 25th April 2022 22:36:36
title: "Draft 1 Notes Alg Grp Background"
aliases: [Draft 1 Notes Alg Grp Background]
---

Last modified: `=this.file.mday`

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [automorphic form](Unsorted/automorphic%20form.md)

---

# Classical Algebraic Groups over Archimedean fields

Parabolics:
![](attachments/Pasted%20image%2020220425222957.png)
Unipotent radicals:
![](attachments/Pasted%20image%2020220425223112.png)

Example of parabolics and unipotent radical:
![](attachments/Pasted%20image%2020220425223332.png)

# Over nonarchimedean local fields

Iwahoris (like Borels) and Parahorics ("parabolic Iwahori", like parabolics):
![](attachments/Pasted%20image%2020220425201345.png)

![](attachments/Pasted%20image%2020220425201458.png)

![](attachments/Pasted%20image%2020220425201421.png)
![](attachments/Pasted%20image%2020220425201429.png)

![](attachments/Pasted%20image%2020220425201636.png)

## Loop groups
![](attachments/Pasted%20image%2020220425201712.png)

![](attachments/Pasted%20image%2020220425201820.png)
![](attachments/Pasted%20image%2020220425201802.png)
![](attachments/Pasted%20image%2020220426001305.png)