def __init__(self, cartan_type, B):
r"""
Initialize ``self``.
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1],[2,2]]); KRT
Tensor product of Kirillov-Reshetikhin tableaux of type ['A', 3, 1] and factor(s) ((3, 1), (2, 2))
sage: TestSuite(KRT).run() # long time
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[2,2]])
sage: TestSuite(KRT).run() # long time
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[3,1]])
sage: TestSuite(KRT).run() # long time
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[4,3]])
sage: TestSuite(KRT).run() # long time
"""
self.dims = B
self.letters = CrystalOfLetters(cartan_type.classical())
tensor_prod = tuple(KirillovReshetikhinTableaux(cartan_type, rect_dims[0], rect_dims[1])
for rect_dims in B)
FullTensorProductOfRegularCrystals.__init__(self, tensor_prod, cartan_type=cartan_type)
# This is needed to override the module_generators set in FullTensorProductOfRegularCrystals
self.module_generators = HighestWeightTensorKRT(self)
self.rename("Tensor product of Kirillov-Reshetikhin tableaux of type %s and factor(s) %s"%(\
cartan_type, B))
def __init__(self, cartan_type, B):
r"""
Initialize ``self``.
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1],[2,2]]); KRT
Tensor product of Kirillov-Reshetikhin tableaux of type ['A', 3, 1] and factor(s) ((3, 1), (2, 2))
sage: TestSuite(KRT).run() # long time
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[2,2]])
sage: TestSuite(KRT).run() # long time
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[3,1]])
sage: TestSuite(KRT).run() # long time
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D',4,1], [[4,3]])
sage: TestSuite(KRT).run() # long time
"""
self.dims = B
self.letters = CrystalOfLetters(cartan_type.classical())
tensor_prod = tuple(
KirillovReshetikhinTableaux(cartan_type, rect_dims[0],
rect_dims[1]) for rect_dims in B)
FullTensorProductOfRegularCrystals.__init__(self,
tensor_prod,
cartan_type=cartan_type)
# This is needed to override the module_generators set in FullTensorProductOfRegularCrystals
self.module_generators = HighestWeightTensorKRT(self)
self.rename("Tensor product of Kirillov-Reshetikhin tableaux of type %s and factor(s) %s"%(\
cartan_type, B))
def __init__(self, cartan_type, B, biject_class):
r"""
Construct a tensor product of KR tableaux.
INPUT:
- ``cartan_type`` -- The crystal type and n value
- ``B`` -- An (ordered) list of dimensions
- ``biject_class`` -- The class the bijection creates
The dimensions (i.e. `B`) is a list whose entries are lists of the
form `[r, s]` which correspond to a tableau with `r` rows and `s`
columns (or of shape `[r]*s`) and corresponds to a
Kirillov-Reshetikhin crystal `B^{r,s}`.
TESTS::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,2]]); HW # indirect doctest
Highest weight tensor product of Kirillov-Reshetikhin tableaux of type ['A', 3, 1] and tableau shape(s) [[1, 1, 1], [2, 2]]
"""
assert cartan_type.is_affine()
self.affine_ct = cartan_type
self.dims = B
self.letters = CrystalOfLetters(cartan_type)
self._bijection_class = biject_class
tensorProd = []
for rectDims in B:
tensorProd.append(KirillovReshetikhinTableaux(self.letters.cartan_type(), rectDims[0], rectDims[1]))
FullTensorProductOfRegularCrystals.__init__(self, tuple(tensorProd))
def __init__(self, cartan_type, B, biject_class):
r"""
Construct a tensor product of KR tableaux.
INPUT:
- ``cartan_type`` -- The crystal type and n value
- ``B`` -- An (ordered) list of dimensions
- ``biject_class`` -- The class the bijection creates
The dimensions (i.e. `B`) is a list whose entries are lists of the
form `[r, s]` which correspond to a tableau with `r` rows and `s`
columns (or of shape `[r]*s`) and corresponds to a
Kirillov-Reshetikhin crystal `B^{r,s}`.
TESTS::
sage: HW = HighestWeightTensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1], [2,2]]); HW # indirect doctest
Highest weight tensor product of Kirillov-Reshetikhin tableaux of type ['A', 3, 1] and tableau shape(s) [[1, 1, 1], [2, 2]]
"""
assert cartan_type.is_affine()
self.affine_ct = cartan_type
self.dims = B
self.letters = CrystalOfLetters(cartan_type)
self._bijection_class = biject_class
tensorProd = []
for rectDims in B:
tensorProd.append(
KirillovReshetikhinTableaux(self.letters.cartan_type(),
rectDims[0], rectDims[1]))
FullTensorProductOfRegularCrystals.__init__(self, tuple(tensorProd))
def tensor_product_of_kirillov_reshetikhin_crystals(self):
"""
Return the corresponding tensor product of Kirillov-Reshetikhin
crystals.
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[3,1],[2,2]])
sage: KRT.tensor_product_of_kirillov_reshetikhin_crystals()
Full tensor product of the crystals [Kirillov-Reshetikhin crystal of type ['A', 3, 1] with (r,s)=(3,1),
Kirillov-Reshetikhin crystal of type ['A', 3, 1] with (r,s)=(2,2)]
TESTS::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[4,1], [3,3]])
sage: KR1 = crystals.KirillovReshetikhin(['D', 4, 1], 4, 1)
sage: KR2 = crystals.KirillovReshetikhin(['D', 4, 1], 3, 3)
sage: T = crystals.TensorProduct(KR1, KR2)
sage: T == KRT.tensor_product_of_kirillov_reshetikhin_crystals()
True
sage: T is KRT.tensor_product_of_kirillov_reshetikhin_crystals()
True
"""
return FullTensorProductOfRegularCrystals(
tuple(x.kirillov_reshetikhin_crystal() for x in self.crystals),
cartan_type=self.cartan_type())
def _module_generators_brute_force(self):
"""
Return the module generators of ``self`` by brute force searching
through all elements of ``self`` as a Cartesian product.
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[1,3], [2,1]])
sage: tuple(KRT.module_generators)
([[1, 1, 1]] (X) [[1], [2]], [[1, 1, 3]] (X) [[1], [2]])
sage: KRT._module_generators_brute_force()
([[1, 1, 1]] (X) [[1], [2]], [[1, 1, 3]] (X) [[1], [2]])
"""
index_set = self.cartan_type().classical().index_set()
return tuple(x for x in FullTensorProductOfRegularCrystals.__iter__(self)
if x.is_highest_weight(index_set))
def _module_generators_brute_force(self):
"""
Return the module generators of ``self`` by brute force searching
through all elements of ``self`` as a Cartesian product.
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A',3,1], [[1,3], [2,1]])
sage: tuple(KRT.module_generators)
([[1, 1, 1]] (X) [[1], [2]], [[1, 1, 3]] (X) [[1], [2]])
sage: KRT._module_generators_brute_force()
([[1, 1, 1]] (X) [[1], [2]], [[1, 1, 3]] (X) [[1], [2]])
"""
index_set = self.cartan_type().classical().index_set()
return tuple(x for x in FullTensorProductOfRegularCrystals.__iter__(self)
if x.is_highest_weight(index_set))