Dynkin diagrams from Lie algebras, and vice versa - Lec 16 - Frederic Schuller

This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller

[EivindDahl]

This guy is among the most organised lecturers I have ever seen

[ericvilas]

When he pointed out that the points at the origin of the root map corresponded to the 2-dimensional Cartan subalgebra, everything clicked. This _really helps_ with understanding particle physics.
(btw, the algebra is su(3), in case people didn't realize)

[tataltsal]

A geometric meaning of the Weyl transformation is a simple reflection. I think mentioning this would have been awesome.

[millerfour]

6:09, 15:20, 36:54, 39:50, 48:14, 1:02:45 (no need to explicitly calculate dual killing form), 1:11:26, 1:14:27 (take all possible “horizontal reflections”), 1:31:02, 1:36:36, 1:37:40

[vadimostapenko]

Very nice and tasty way to present those computations. Thank ytou a lot!

[reinerwilhelms-tricarico]

The captions displayed the Weyl group and transformations as wild group/transformations - consistently. 😂

[somasundaramsankaranarayan]

At 47:47, it was wrongly assumed that the three vectors are linearly independent, when indeed they are linearly dependent.

[rodrigomendes]

I made the calculations for the killing form and found k22=0. Don't know where I'm wrong. The calculations:

K22=C^{m}_{2 n}C^{n}_{2 m}
=C^{1}_{2 n}C^{n}_{2 1} + C^{2}_{2 n}C^{n}_{2 2} + C^{3}_{2 n}
For the first term, n=3 but C^{3}_{2 1} = 0. The second possibility is on the second term n=2, but C^{1}_{2 2} = 0. So, the first two term goes to zero. The second term is zero and the third is zero to a think similar to the first that I made. So, k22= 0

[borispawilowski]

At 01:16:00 one can actually find s_\pi_1 (\pi_1+\pi_2) by linearity by using the previous calculus

[varunmenon]

At 1:25:28 why are the roots evaluated at the basis vectors of H the same numbers on the root diagram? Is the root diagram necessarily w.r.t the h1 h2 basis?

[joelcurtis]

When he draws the picture of the fundamental roots around 1:14:00, what is the space we're in? What is represented by each axis? Are they just the real numbers, since this is the realification of the dual space of the cartan subalgebra H?

[luisgeniole]

Did you know that german professors work part time as window cleaners?

[abomohamed]

I want to know is that there is a computer program by formal calculation that allows to build the dynkin diagram. thanks

[andreemcaldas]

At 50:36. After you know that alpha is zero, you are back to the first, already analyzed case.

[shanborlangbynnud]

I don't know what magic he's excecuting at 1:12:57 can anyone help.