def _call_(self, x):
r"""
Return the image of ``x`` in the rigged configuration model
of `B(\infty)`.
EXAMPLES::
sage: RC = crystals.infinity.RiggedConfigurations(['A',3])
sage: T = crystals.infinity.Tableaux(['A',3])
sage: phi = RC.coerce_map_from(T)
sage: x = T.an_element().f_string([2,2,1,1,3,2,1,2,1,3])
sage: y = phi(x); ascii_art(y)
-4[ ][ ][ ][ ]-2 -3[ ][ ][ ]-1 -1[ ][ ]-1
-2[ ]-1
sage: (~phi)(y) == x
True
"""
conj = x.to_tableau().conjugate()
ct = self.domain().cartan_type()
act = ct.affine()
TP = TensorProductOfKirillovReshetikhinTableaux(act, [[r,1] for r in conj.shape()])
elt = TP(pathlist=[reversed(row) for row in conj])
if ct.type() == 'A':
bij = KRTToRCBijectionTypeA(elt)
elif ct.type() == 'B':
bij = MLTToRCBijectionTypeB(elt)
elif ct.type() == 'C':
bij = KRTToRCBijectionTypeC(elt)
elif ct.type() == 'D':
bij = MLTToRCBijectionTypeD(elt)
else:
raise NotImplementedError("bijection of type {} not yet implemented".format(ct))
return self.codomain()(bij.run())
def KRTToRCBijection(tp_krt):
r"""
Return the correct KR tableaux to rigged configuration bijection helper class.
TESTS::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bijection import KRTToRCBijection
sage: bijection = KRTToRCBijection(KRT(pathlist=[[5,2]]))
"""
ct = tp_krt.cartan_type()
typ = ct.type()
if ct.is_untwisted_affine():
if typ == 'A':
return KRTToRCBijectionTypeA(tp_krt)
if typ == 'B':
return KRTToRCBijectionTypeB(tp_krt)
if typ == 'C':
return KRTToRCBijectionTypeC(tp_krt)
if typ == 'D':
return KRTToRCBijectionTypeD(tp_krt)
if typ == 'E':
if ct.classical().rank() < 8:
return KRTToRCBijectionTypeE67(tp_krt)
#if typ == 'F':
#if typ == 'G':
else:
if typ == 'BC': # A_{2n}^{(2)}
return KRTToRCBijectionTypeA2Even(tp_krt)
typ = ct.dual().type()
if typ == 'BC': # A_{2n}^{(2)\dagger}
return KRTToRCBijectionTypeA2Dual(tp_krt)
if typ == 'B': # A_{2n-1}^{(2)}
return KRTToRCBijectionTypeA2Odd(tp_krt)
if typ == 'C': # D_{n+1}^{(2)}
return KRTToRCBijectionTypeDTwisted(tp_krt)
#if typ == 'F': # E_6^{(2)}
if typ == 'G': # D_4^{(3)}
return KRTToRCBijectionTypeDTri(tp_krt)
raise NotImplementedError
