Dear Andrew,
On Mon, Nov 10, 2014 at 04:24:40AM -0800, Andrew wrote:
>
> Yes, I agree, using coxeter3 will almost certainly be much more efficient.
> I had a brief look at this and thought it looked two hard since I have only
> a fleeting interest in this:)
>
> In terms of syntax, chevie has a *LeftCells* function that returns all of
> the cells of the Coxeter group, together with the corresponding
> mu-coefficients -- this, I think, is equivalent to the information that
> coxeter3 returns as it sounds like coxeter3 returns the W-graph for the
> cell representation.
>
> In terms of the suggested syntax, I think that this is partly driven by
> what coxeter3 actually does. I was thinking of something like:
>
> sage: W=CoxeterGroup("A3"); w=W.an_element()
> sage: W.left_cell( w ) # left cell containing w
> sage: W.left_cells() # all left cells -- as chevie's LeftCells(W) does now
>
>
> In particular, rather the computing the complete decomposition of the
> Coxeter group into a disjoint union of cells I think that it would be
> useful to be able to compute only the cell containing a particular element.
You should look at the latest version of chevie
http://webusers.imj-prg.fr/~jean.michel/gap3/gap3-jm4.tar.gz
or
http://webusers.imj-prg.fr/~jean.michel/gap3/gap3-jm5.tar.gz
where I implemented the latest stuff of Meinolf Geck and Abbie Hall.
I can give the elements of the left cell containing a given element of E8 in
less than 2 minutes.
Here is an example in E7:
gap>W:=CoxeterGroup("E",7);;
gap> LeftCell(W,Random(W));time;
LeftCell<E7: duflo=18,21,45,53 character=phi{378,14}>
40
40 milliseconds!
Best regards,
------------------------------------------------------------------------------
Jean MICHEL, Groupes et representations, IMJ-PRG UMR7586 tel.(33)157279144
Bureau 639 Bat. Sophie Germain Case 7012 - 75205 PARIS Cedex 13
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