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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 1st 2020

    moved the discussion of the Lie algebra 𝔰𝔲(2)\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)

    diff, v18, current

    • 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 SU(2)\mathrm{SU}(2) is the sum of the 3d irrep and the 3d trivial rep:

    443113RO(Sp(1)) \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?

    diff, v19, current

    • 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.