Central polynumbers and SL(2) / SU(2) characters | Math Foundations 235 | N J Wildberger
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- čas přidán 27. 07. 2024
- Let's consider a novel approach to the representation theory of the Lie groups SL(2) and SU(2), which play a major role both in mathematics and physics. We give an elementary algebraic approach to this story which is, to my knowledge, not found in any of the many standard texts and articles which try to explain this subject. The general polynumbers C_n which appeared in the last lecture turn out to play a truly central role in this subject.
We are utilizing our mset approach to arithmetic, augmented by the particle / anti particle duality which we have taken from modern physics and placed centrally in our arithmetic with integral polynumbers.
This orientation is strongly motivated by our insistence that pure mathematics be done correctly! In other words, that "completed infinite processes" and the associated fantasy of "arithmetic with real numbers" have to be avoided; and so we want to frame everything in terms of rational numbers and their complex number extensions. Lots to think about here for students of both Lie theory and modern physics.
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I have been looking forward to this for a long time
This is magnificent! I have had four weeks of huge anticipation since MF234 was published, and this was a delight to watch beyond even the high expectations I already had!
I love when we roll up our sleeves and make some exact calculations ...
This video made me dig out a book on invariant theory from my old bookmarks folder.
Absolutely fantastic Norman! Your ability to think independently is such a breath of fresh air! I can't wait for the net video on this topic. Many many thanks.
Great stuff. Thank you very much.
Well, surprise! I could follow this 😊