This is now https://trac.sagemath.org/ticket/31391
dwb...@gmail.com schrieb am Samstag, 13. Februar 2021 um 04:59:50 UTC+1:
> 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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