[Jprogramming] Musings on permutation vectors

[John Randall]

R&S HUI wrote:
> Hmm, that means you can transform an operation
> involving the monads /: \: |. on permutations into
> an isomorphic operation using the monads j. + -
> on complex vectors.
>
> The relationship to complex numbers was not mentioned
> in the introductory abstract algebra course that I
> took many years ago.  Perhaps it is "obvious".
>
>

I don't think it's deep.  Basically:

- Every finite group has a faithful representation as a permutation group.

- The dihedral group has a faithful irreducible O(2) representation.

- Identifying the complex numbers with the real plane, we can
conveniently identify the images of the generators with J primitives.

If you could find another handy representation of the dihedral group,
you would have another set of identities.

Best wishes,

John