Hi Nicolas and Dan,
On Wed, Jan 12, 2011 at 12:06:40AM -0800, Anne Schilling wrote:
(1) For type B and D there exist tableaux with spin columns
of half width, but they are currently not yet implemented in sage.
In principle, one can construct them using the TensorProductOfCrystals,
but it might be nice to be able to do something like
sage: T = CrystalOfTableaux(['B',3], shape = [3/2,1/2,1/2])
Currently this would have to be done as
sage: S = CrystalOfSpins(['B',3])
sage: B = CrystalOfTableaux(['B',3], shape = [1])
sage: T = TensorProductOfCrystals(S,B, generators =
[[S.module_generators[0], B.module_generators[0]]])
I guess CrystalOfTableaux(['B',3], shape = [3/2,1/2,1/2]) could return
an object of a new class looking like:
class CrystalOfTableauxWithSpin(TensorProductOfCrystals):
def _repr_(self):
...
class Element(TensorProductOfCrystals.Element):
def _repr_(self):
...
def latex(self):
...
(I don't have the specifics of the TensorProductOfCrystals classes on
top of my head, so there probably is some little adaptation to do).
Yes, this sounds good in principle.
What would be the best way to display columns of 1/2 width and mark them as
spin?
Could you choose a typical element, and try to draw here what could be
a good ascii art picture of it? And possibly provide some links to
articles online with some nice latex pictures of such?
Perhaps
+--+----+----+----+
| 1| 2 | 3 | 0 |
+--+----+----+----+
| 2| -3 | -3 |
+--+----+----+
|-3| -2 |
+--+----+
where the first column is a spin column of width 1/2.
In latex this is example 8.4.2 in Hong and Kang "Introduction to Quantum groups
and crystal bases" page 196.
Cheers,
Anne
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