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    • CommentRowNumber1.
    • CommentAuthorsgarush
    • CommentTimeApr 10th 2018

    In the article exterior+algebra, in sect. 2, subsection In General, it says that the nth exterior power of an object VV is the cokernel of the antisymmetrization operator

    P A=1n! σS nsgn(σ)σ. P_{A} = \frac{1}{n!} \sum_{\sigma \in S_{n}} \mathrm{sgn}(\sigma) \sigma.

    Shouldn’t the exterior algebra be the image of this operator? If so, I am happy to edit the article accordingly.

    • CommentRowNumber2.
    • CommentAuthorsgarush
    • CommentTimeApr 10th 2018

    It looks like in schur+functor what is used is the cokernel of 1P A1 - P_A – is this correct?

  1. Yes you’re correct. At least in the context of vector spaces over a field of characteristic 00, Λ nV\Lambda^{n}V is the image of P AP_A, the coimage of P AP_A, the kernel of 1P A1-P_A and the cokernel of 1P A1-P_A. So the statement at Schur functor is correct.

    • CommentRowNumber4.
    • CommentAuthorsgarush
    • CommentTimeApr 10th 2018

    Great, thanks. I guess I’ll edit the article to bring it in line with Schur functor.