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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 1st 2020

moved the discussion of the Lie algebra $\mathfrak{su}(2)$ out of the middle of “Properties – General” into its own subsection “Properties – Lie algebra”.

Will copy this also over to su(2)

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 1st 2020

Hm, strange. The above edit comment was for SU(2) (capital)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 8th 2020

Just something elementary:

unless I am mixed up, the wedge square of the 4d irrep of $\mathrm{SU}(2)$ is the sum of the 3d irrep and the 3d trivial rep:

$\mathbf{4}\wedge \mathbf{4} \;\simeq\; 3 \cdot \mathbf{1} \;\oplus\; 1 \cdot \mathbf{3} \;\;\;\in\; \mathrm{RO}(\mathrm{Sp}(1))$

(see Sandbox) What would be a classical fact/text to refer to for this?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 13th 2020

in any case, I have added the statement and proof of this elementary fact at SU(2) here

(just to remark that the automatic announcement mechanism gets confused with the capitalization: all edits to SU(2) seem to get announced here in the thread on su(2))

1. Thanks for raising, I have now fixed this. Just a reminder that I may miss this kind of thing unless it is flagged in an obvious place for me to see it.