You can construct the two spin crystals using crystals.SpinsMinus("D5") and
crystals.SpinsPlus("D5").
If you want other spin weights, you can tensor these crystals with an
orthogonal crystal. But
the method you tried should either work or fail gracefully instead of
returning a wrong result.
Daniel Bump
On Friday, February 12, 2021 at 9:49:42 AM UTC-8 axio...@yahoo.de wrote:
> Thank you, that explains it to me!
>
> Currently, the code that translates dominant weights to crystals is (line
> 174 of highest_weight_crystals.py)
>
> sh = sum([[i]*c for i,c in dominant_weight], [])
> sh = Partition(reversed(sh))
> return CrystalOfTableaux(cartan_type, shape=sh.conjugate())
>
> So I guess there might also be a less visible problem for type B, and in
> the case of the spin weights we should rather be returning CrystalOfSpins,
> CrystalOfSpinsPlus, CrystalOfSpinsMinus.
>
> So, maybe we should use dominant.to_ambient?
>
> Martin
> dwb...@gmail.com schrieb am Freitag, 12. Februar 2021 um 16:52:02 UTC+1:
>
>> It looks like Sage is constructing the wrong crystals for the two spin
>> weights. D5 does have
>> two irreducible representations of dimensions 210 and 126 but their
>> highest weights are not
>> the spin weights s1=(1/2,1/2,1/2,1/2,1/2) and s2=(1/2,1/2,1/2,1/2,-1/2)
>> which are the two
>> fundamental weights. Instead the highest weights of the representations
>> with these degrees
>> 210 and 126 are s1+s2 and 2*s1.
>>
>> This appears to me to be a bug in the crystal code.
>>
>> Daniel Bump
>> On Thursday, February 11, 2021 at 9:30:15 AM UTC-8 axio...@yahoo.de
>> wrote:
>>
>>> I am confused about the following result:
>>>
>>> sage: ct = CartanType(["D", 5])
>>> sage: L = RootSystem(ct).weight_lattice()
>>> sage: La = L.fundamental_weights();
>>> sage: [L.weyl_dimension(wt) for wt in La]
>>> [10, 45, 120, 16, 16]
>>> sage: [crystals.HighestWeight(wt).q_dimension().subs(q=1) for wt in La]
>>> [10, 45, 120, 210, 126]
>>>
>>> Am I doing something wrong or is this a bug? I would expect the former
>>> dimensions, but I am not versed enough in the theory to be sure that I did
>>> not make a mistake myself. The discrepancy seems to occur only with type D.
>>>
>>> All the best,
>>>
>>> Martin
>>>
>>
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