def __init__(self, parent, list=[[]], **options):
r"""
Construct a TensorProductOfKirillovReshetikhinTableauxElement.
INPUT:
- ``parent`` -- Parent for this element
- ``list`` -- The list of KR tableaux elements
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 3, 1], [[1, 1], [2, 1], [1, 1], [2, 1], [2, 1], [2, 1]])
sage: T = KRT(pathlist=[[2], [4, 1], [3], [4, 2], [3, 1], [2, 1]])
sage: T
[[2]] (X) [[1], [4]] (X) [[3]] (X) [[2], [4]] (X) [[1], [3]] (X) [[1], [2]]
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 3, 1], [[3,3], [2,1]])
sage: T = KRT(pathlist=[[3, 2, 1, 4, 2, 1, 4, 3, 1], [2, 1]])
sage: T
[[1, 1, 1], [2, 2, 3], [3, 4, 4]] (X) [[1], [2]]
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2, 1], [1, 1], [1, 1], [1, 1]])
sage: T = KRT(pathlist=[[3,2], [1], [-1], [1]])
sage: T
[[2], [3]] (X) [[1]] (X) [[-1]] (X) [[1]]
sage: TestSuite(T).run()
"""
if "pathlist" in options:
pathlist = options["pathlist"]
TensorProductOfRegularCrystalsElement.__init__(
self, parent,
[parent.crystals[i](*tab) for i, tab in enumerate(pathlist)])
else:
TensorProductOfRegularCrystalsElement.__init__(self, parent, list)
def __init__(self, parent, list=[[]], **options):
r"""
Construct a TensorProductOfKirillovReshetikhinTableauxElement.
INPUT:
- ``parent`` -- Parent for this element
- ``list`` -- The list of KR tableaux elements
EXAMPLES::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 3, 1], [[1, 1], [2, 1], [1, 1], [2, 1], [2, 1], [2, 1]])
sage: T = KRT(pathlist=[[2], [4, 1], [3], [4, 2], [3, 1], [2, 1]])
sage: T
[[2]] (X) [[1], [4]] (X) [[3]] (X) [[2], [4]] (X) [[1], [3]] (X) [[1], [2]]
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 3, 1], [[3,3], [2,1]])
sage: T = KRT(pathlist=[[3, 2, 1, 4, 2, 1, 4, 3, 1], [2, 1]])
sage: T
[[1, 1, 1], [2, 2, 3], [3, 4, 4]] (X) [[1], [2]]
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2, 1], [1, 1], [1, 1], [1, 1]])
sage: T = KRT(pathlist=[[3,2], [1], [-1], [1]])
sage: T
[[2], [3]] (X) [[1]] (X) [[-1]] (X) [[1]]
sage: TestSuite(T).run()
"""
if "pathlist" in options:
pathlist = options["pathlist"]
TensorProductOfRegularCrystalsElement.__init__(self, parent,
[parent.crystals[i](*tab) for i, tab in enumerate(pathlist)])
else:
TensorProductOfRegularCrystalsElement.__init__(self, parent, list)
def e(self, i):
r"""
Calculate the action of `e_i` on ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).e(1)
[[1], [3], [-4], [-2]]
sage: KRT([-1, -4, 3, 2]).e(3)
"""
half = TensorProductOfRegularCrystalsElement.e(self, i)
if half is None:
return None
return TensorProductOfRegularCrystalsElement.e(half, i)
def e(self, i):
r"""
Calculate the action of `e_i` on ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).e(1)
[[1], [3], [-4], [-2]]
sage: KRT([-1, -4, 3, 2]).e(3)
"""
half = TensorProductOfRegularCrystalsElement.e(self, i)
if half is None:
return None
return TensorProductOfRegularCrystalsElement.e(half, i)
def __init__(self, parent, list, **options):
r"""
Initialize ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['A', 4, 1], 2, 1)
sage: elt = KRT([4, 3]); elt
[[3], [4]]
sage: TestSuite(elt).run()
"""
# Make sure we are a list of letters
if list != [] and type(list[0]) is not parent.letters.element_class:
list = [parent.letters(x) for x in list]
TensorProductOfRegularCrystalsElement.__init__(self, parent, list)
def __init__(self, parent, list, **options):
r"""
Initialize ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['A', 4, 1], 2, 1)
sage: elt = KRT([4, 3]); elt
[[3], [4]]
sage: TestSuite(elt).run()
"""
# Make sure we are a list of letters
if list != [] and type(list[0]) is not parent.letters.element_class:
list = [parent.letters(x) for x in list]
TensorProductOfRegularCrystalsElement.__init__(self, parent, list)
def f(self, i):
r"""
Calculate the action of `f_i` on ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).f(1)
sage: KRT([-1, -4, 3, 2]).f(3)
[[2], [4], [-3], [-1]]
"""
half = TensorProductOfRegularCrystalsElement.f(self, i)
if half is None:
return None
return TensorProductOfRegularCrystalsElement.f(half, i)
def f(self, i):
r"""
Calculate the action of `f_i` on ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).f(1)
sage: KRT([-1, -4, 3, 2]).f(3)
[[2], [4], [-3], [-1]]
"""
half = TensorProductOfRegularCrystalsElement.f(self, i)
if half is None:
return None
return TensorProductOfRegularCrystalsElement.f(half, i)
def epsilon(self, i):
r"""
Compute `\epsilon_i` of ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).epsilon(1)
1
sage: KRT([-1, -4, 3, 2]).epsilon(3)
0
"""
return TensorProductOfRegularCrystalsElement.epsilon(self, i) / 2
def phi(self, i):
r"""
Compute `\phi_i` of ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).phi(1)
0
sage: KRT([-1, -4, 3, 2]).phi(3)
1
"""
return TensorProductOfRegularCrystalsElement.phi(self, i) / 2
def epsilon(self, i):
r"""
Compute `\epsilon_i` of ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).epsilon(1)
1
sage: KRT([-1, -4, 3, 2]).epsilon(3)
0
"""
return TensorProductOfRegularCrystalsElement.epsilon(self, i) / 2
def phi(self, i):
r"""
Compute `\phi_i` of ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 1)
sage: KRT([-1, -4, 3, 2]).phi(1)
0
sage: KRT([-1, -4, 3, 2]).phi(3)
1
"""
return TensorProductOfRegularCrystalsElement.phi(self, i) / 2
def f(self, i):
r"""
Return the action of `f_i` on ``self``.
EXAMPLES::
sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
sage: T = KRT(pathlist=[[4,3]])
sage: T.f(1)
sage: T.f(4)
[[-4], [4]]
"""
if i != 0:
return TensorProductOfRegularCrystalsElement.f(self, i)
return None
def weight(self):
"""
Return the weight of ``self``.
EXAMPLES::
sage: B = crystals.KirillovReshetikhin(['A',2,1], 1,1)
sage: P = RootSystem(['A',2,1]).weight_lattice(extended=True)
sage: La = P.fundamental_weights()
sage: C = crystals.KyotoPathModel(B, La[0])
sage: mg = C.module_generators[0]
sage: mg.weight()
Lambda[0]
sage: mg.f_string([0,1,2]).weight()
Lambda[0] - delta
"""
wt = TensorProductOfRegularCrystalsElement.weight(self)
return wt + self[-1].Epsilon()
def weight(self):
"""
Return the weight of ``self``.
EXAMPLES::
sage: B = crystals.KirillovReshetikhin(['A',2,1], 1,1)
sage: P = RootSystem(['A',2,1]).weight_lattice(extended=True)
sage: La = P.fundamental_weights()
sage: C = crystals.KyotoPathModel(B, La[0])
sage: mg = C.module_generators[0]
sage: mg.weight()
Lambda[0]
sage: mg.f_string([0,1,2]).weight()
Lambda[0] - delta
"""
wt = TensorProductOfRegularCrystalsElement.weight(self)
return wt + self[-1].Epsilon()
def f(self, i):
"""
Perform the action of `f_i` on ``self``.
.. TODO::
Implement a direct action of `f_0` without moving to KR crystals.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 2,2)
sage: KRT.module_generators[0].f(0)
[[1, 1], [2, -1]]
"""
if i == 0:
ret = self.to_Kirillov_Reshetikhin_crystal().f0()
if ret is None:
return None
return ret.to_Kirillov_Reshetikhin_tableau()
return TensorProductOfRegularCrystalsElement.f(self, i)
def f(self, i):
"""
Perform the action of `f_i` on ``self``.
.. TODO::
Implement a direct action of `f_0` without moving to KR crystals.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 2,2)
sage: KRT.module_generators[0].f(0)
[[1, 1], [2, -1]]
"""
if i == 0:
ret = self.to_Kirillov_Reshetikhin_crystal().f0()
if ret is None:
return None
return ret.to_Kirillov_Reshetikhin_tableau()
return TensorProductOfRegularCrystalsElement.f(self, i)
