[GAP Forum] unexpected behavior of SchurCoverOfSymmetricGroup

[Alexander Hulpke]

Der Forum,

> On Sep 3, 2015, at 7:44 AM, Benjamin Sambale <benjamin.sambale at gmail.com> wrote:
> 
> the command SchurCoverOfSymmetricGroup can be used to define the two double covers of a symmetric group. According to the manual:
> 
> "+1 gives a group where the preimage of an adjacent transposition (i,i+1) has order 4"
> 
> I thought that the convention is just the other way around: in the "+" type cover the transpositions lift to involutions.

Looking through the literature going back to Schur’s original papers it seems that what is considered the ``canonical’’ or ``+1’’ cover is not consistent. GAP’s convention thus represents a necessary choice made by the code authors which I find hard to criticise.

We will add a warning line to the manual to alert users to this difference of conventions, thus hopefully avoiding further confusion.

Best wishes,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
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