root system

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root system

attachments/Pasted%20image%2020220420143805.png

Borel subgroups containing a fixed torus \(T\) biject with positive root systems.

attachments/Pasted%20image%2020220420143944.png attachments/Pasted%20image%2020220420143952.png

Langlands dual

attachments/Pasted%20image%2020220420144138.png

Cartan involution

attachments/Pasted%20image%2020220420144157.png

Examples

A1 x A1

attachments/Pasted%20image%2020220526171240.png

A2

attachments/Pasted%20image%2020220526171227.png attachments/Pasted%20image%2020220526171132.png

B2

attachments/Pasted%20image%2020220526171146.png

G2

attachments/Pasted%20image%2020220526171215.png

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