On Sun, Jan 23, 2011 at 09:57:36PM -0800, Anne Schilling wrote:
> One problem with this is, that the list of shapes option is heavily
> used in the construction of KR crystals, as first their classical
> crystal structure is defined and then the 0-arrows are constructed
> on top of this.
Sure.
> The final result is not a direct sum of crystals, so I would not
> like to have this as the data structure. It is only an intermediate
> trick to construct them.
This technical information seems fairly encapsulated to me, since the
classical crystal D and its affine counterpart C are clearly
separated. Indeed, the relation between elements of C and of D is that
x contains an element of D (in x.value/x.lift()) [1], not that x is an
element of D (as if there was an inheritance relation) [2].
So D can be a direct sum without imposing C to be.
Besides, the direct sum approach would allow for creating affine
crystals where the classical structure has several highest vectors of
same weight (or does the current code already uses a trick for those?)
Cheers,
Nicolas
[1] http://en.wikipedia.org/wiki/Has-a
[2] http://en.wikipedia.org/wiki/Is-a
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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