If denotes the standard representation of , what is the weight diagram of ? Can you guess the weight diagram of ?
Verify that the matrices live in the following weight spaces: Plot these weights and verify that the hexagonal picture from the lecture is correct.
What do you think the weight diagram of the standard 4-dimensional representation of would look like? How do you think the matrices act?
How does decompose into irreps of the -subalgebra spanned by , and ?