On Sun, Mar 27, 2011 at 11:07:58PM -0700, Anne Schilling wrote:
> On 3/27/11 6:27 PM, bump wrote:
> >>I just added a new patch on trac which implements the Schuetzenberger
> >>involution on both words and tableaux and also the promotion operator
> >>on tableaux of arbitrary shape:
> >>
> >>http://trac.sagemath.org/sage_trac/ticket/10446
> >
> >I have the impression this is for Type A only. But the Schutzenberger
> >involution could be implemented for any Cartan type using the crystal.
> >So my question is whether this should actually be a method for
> >CrystalOfTableauxElements instead of tableaux.
>
> Yes, it also exists for any Cartan type, but my impression was that then
> it is called Lusztig involution. My plan is indeed to eventually implement
> the Lusztig involution in CrystalOfTableauxElements. What do you think?
I don't have the details on top of my head, so I'll just speak vaguely
here. Unless the algorithms are basically identical, it seems very
reasonable to have a generic (type-free?) implementation in
CrystalOfTableauxElements using the crystal structure, and a
specialized implementation in Tableaux using the combinatorics of
tableaux. And to include some tests that compare the results and check
their consistency!
As for posets, I don't know. I would tend to first write a draft of
the method in Posets, and then decide if the interfaces and
implementations are similar enough to be shared or not.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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