Trac #13872 - Implemented RC<->KR tableaux bijections for non-exceptional types

Author: Travis Scrimshaw

src/doc/en/reference/combinat/rc_bijections.rst

@@ -0,0 +1,17 @@
+Rigged Configuration Bijections
+===============================
+
+.. toctree::
+   :maxdepth: 1
+
+   ../sage/combinat/rigged_configurations/bijection
+   ../sage/combinat/rigged_configurations/bij_abstract_class
+   ../sage/combinat/rigged_configurations/bij_type_A
+   ../sage/combinat/rigged_configurations/bij_type_B
+   ../sage/combinat/rigged_configurations/bij_type_C
+   ../sage/combinat/rigged_configurations/bij_type_D
+   ../sage/combinat/rigged_configurations/bij_type_A2_odd
+   ../sage/combinat/rigged_configurations/bij_type_A2_even
+   ../sage/combinat/rigged_configurations/bij_type_A2_dual
+   ../sage/combinat/rigged_configurations/bij_type_D_twisted
+

src/doc/en/reference/combinat/rigged_configurations.rst

@@ -2,7 +2,7 @@ Rigged Configurations
 =====================
 
 .. toctree::
-   :maxdepth: 2
+   :maxdepth: 1
 
    ../sage/combinat/rigged_configurations/rigged_configurations
    ../sage/combinat/rigged_configurations/rigged_configuration_element
@@ -15,8 +15,5 @@ Rigged Configurations
 
    ../sage/combinat/rigged_configurations/rigged_partition
 
-   ../sage/combinat/rigged_configurations/bijection
-   ../sage/combinat/rigged_configurations/bij_abstract_class
-   ../sage/combinat/rigged_configurations/bij_type_A
-   ../sage/combinat/rigged_configurations/bij_type_D
+   rc_bijections
 

src/sage/combinat/crystals/kirillov_reshetikhin.py

@@ -397,9 +397,9 @@ def _repr_(self):
         """
         return "Kirillov-Reshetikhin crystal of type %s with (r,s)=(%d,%d)" % (self.cartan_type(), self.r(), self.s())
 
-    def _element_constructor_(self, *value, **options):
+    def _element_constructor_(self, *args, **options):
         """
-        Construct an element of ``self`` from ``elt``.
+        Construct an element of ``self`` from the input.
 
         EXAMPLES::
 
@@ -408,10 +408,10 @@ def _element_constructor_(self, *value, **options):
             [[1], [2]]
         """
         from sage.combinat.rigged_configurations.kr_tableaux import KirillovReshetikhinTableauxElement
-        if isinstance(value[0], KirillovReshetikhinTableauxElement):
-            elt = value[0]
+        if isinstance(args[0], KirillovReshetikhinTableauxElement):
+            elt = args[0]
             # Check to make sure it can be converted
-            if elt.cartan_type().affine() != self.cartan_type() \
+            if elt.cartan_type() != self.cartan_type() \
               or elt.parent().r() != self._r or elt.parent().s() != self._s:
                 raise ValueError("The Kirillov-Reshetikhin tableau must have the same Cartan type and shape")
 
@@ -424,7 +424,7 @@ def _element_constructor_(self, *value, **options):
             hw_elt = self(rows=rows)
             f_str = reversed(to_hw[1])
             return hw_elt.f_string(f_str)
-        return AffineCrystalFromClassical._element_constructor_(self, *value, **options)
+        return AffineCrystalFromClassical._element_constructor_(self, *args, **options)
 
     @abstract_method
     def classical_decomposition(self):
@@ -614,6 +614,7 @@ def R_matrix(self, K):
         g = { gen1 : gen2 }
         return T1.crystal_morphism(g, acyclic = False)
 
+    @cached_method
     def Kirillov_Reshetikhin_tableaux(self):
         """
         Return the corresponding set of :class:`KirillovReshetikhinTableaux`.
@@ -631,6 +632,7 @@ class KirillovReshetikhinGenericCrystalElement(AffineCrystalFromClassicalElement
     """
     Abstract class for all Kirillov-Reshetikhin crystal elements.
     """
+    @cached_method
     def to_Kirillov_Reshetikhin_tableau(self):
         r"""
         Construct the corresponding
@@ -1638,7 +1640,7 @@ def from_ambient_crystal(self):
         return self.crystal_morphism( pdict_inv, index_set = [j+1 for j in self.cartan_type().classical().index_set()],
                                       automorphism = lambda i : i-1 )
 
-class KR_type_A2Element(AffineCrystalFromClassicalElement):
+class KR_type_A2Element(KirillovReshetikhinGenericCrystalElement):
     r"""
     Class for the elements in the Kirillov-Reshetikhin crystals `B^{r,s}` of type `A_{2n}^{(2)}` for `r<n`
     with underlying classcial algebra `B_n`.
@@ -1985,6 +1987,39 @@ class KR_type_Bn(KirillovReshetikhinGenericCrystal):
         sage: [b.weight() for b in K if b.is_highest_weight([0,2,3])]
         [Lambda[0] - Lambda[1], -2*Lambda[1] + 2*Lambda[3]]
     """
+    def _element_constructor_(self, *args, **options):
+        """
+        Construct an element of ``self``.
+
+        TESTS::
+
+            sage: KRC = KirillovReshetikhinCrystal(['B',3,1], 3, 3)
+            sage: KRT = KirillovReshetikhinTableaux(['B',3,1], 3, 3)
+            sage: elt = KRC.module_generators[1].f_string([3,2,3,1,3,3]); elt
+            [++-, [[2], [0], [-3]]]
+            sage: ret = KRT(elt); ret
+            [[1, 1, 2], [2, 2, -3], [-3, -3, -1]]
+            sage: test = KRC(ret); test
+            [++-, [[2], [0], [-3]]]
+            sage: test == elt
+            True
+        """
+        from sage.combinat.rigged_configurations.kr_tableaux import KirillovReshetikhinTableauxElement
+        if isinstance(args[0], KirillovReshetikhinTableauxElement):
+            elt = args[0]
+            # Check to make sure it can be converted
+            if elt.cartan_type() != self.cartan_type() \
+              or elt.parent().r() != self._r or elt.parent().s() != self._s:
+                raise ValueError("The Kirillov-Reshetikhin tableau must have the same Cartan type and shape")
+
+            to_hw = elt.to_classical_highest_weight()
+            wt = to_hw[0].classical_weight() / 2
+            f_str = reversed(to_hw[1])
+            for x in self.module_generators:
+                if x.classical_weight() == wt:
+                    return x.f_string(f_str)
+            raise ValueError("No matching highest weight element found")
+        return KirillovReshetikhinGenericCrystal._element_constructor_(self, *args, **options)
 
     def classical_decomposition(self):
         r"""
@@ -2276,7 +2311,7 @@ def from_pm_diagram_to_highest_weight_vector(self, pm):
             u = u.f(i)
         return u
 
-class KR_type_CnElement(AffineCrystalFromClassicalElement):
+class KR_type_CnElement(KirillovReshetikhinGenericCrystalElement):
     r"""
     Class for the elements in the Kirillov-Reshetikhin crystals `B^{n,s}` of type `C_n^{(1)}`.
 
@@ -2519,7 +2554,7 @@ def from_pm_diagram_to_highest_weight_vector(self, pm):
             u = u.f(i)
         return u
 
-class KR_type_Dn_twistedElement(AffineCrystalFromClassicalElement):
+class KR_type_Dn_twistedElement(KirillovReshetikhinGenericCrystalElement):
     r"""
     Class for the elements in the Kirillov-Reshetikhin crystals `B^{n,s}` of type `D_{n+1}^{(2)}`.
 
@@ -2679,15 +2714,15 @@ class KR_type_spin(KirillovReshetikhinCrystalFromPromotion):
         sage: all(b.f(0).e(0) == b for b in K if b.phi(0)>0)
         True
     """
-    def _element_constructor_(self, *value, **options):
+    def _element_constructor_(self, *args, **options):
         """
-        Construct an element of ``self`` from ``elt``.
+        Construct an element of ``self`` from the input.
 
         EXAMPLES::
 
             sage: KRT = KirillovReshetikhinTableaux(['D',4,1], 4, 3)
             sage: KRC = KirillovReshetikhinCrystal(['D',4,1], 4, 3)
-            sage: elt = KRT([-3,-4,2,1,-3,-4,2,1,-2,-4,3,1]); elt
+            sage: elt = KRT(-3,-4,2,1,-3,-4,2,1,-2,-4,3,1); elt
             [[1, 1, 1], [2, 2, 3], [-4, -4, -4], [-3, -3, -2]]
             sage: KRC(elt) # indirect doctest
             [++--, [[1], [3], [-4], [-3]]]
@@ -2708,17 +2743,17 @@ def _element_constructor_(self, *value, **options):
             True
         """
         from sage.combinat.rigged_configurations.kr_tableaux import KirillovReshetikhinTableauxElement
-        if isinstance(value[0], KirillovReshetikhinTableauxElement):
-            elt = value[0]
+        if isinstance(args[0], KirillovReshetikhinTableauxElement):
+            elt = args[0]
             # Check to make sure it can be converted
-            if elt.cartan_type().affine() != self.cartan_type() \
+            if elt.cartan_type() != self.cartan_type() \
               or elt.parent().r() != self._r or elt.parent().s() != self._s:
                 raise ValueError("The Kirillov-Reshetikhin tableau must have the same Cartan type and shape")
 
             to_hw = elt.to_classical_highest_weight()
             f_str = reversed(to_hw[1])
             return self.module_generator().f_string(f_str)
-        KirillovReshetikhinCrystalFromPromotion._element_constructor_(self, *value, **options)
+        return KirillovReshetikhinCrystalFromPromotion._element_constructor_(self, *args, **options)
 
     def classical_decomposition(self):
         r"""

src/sage/combinat/crystals/letters.pyx

@@ -442,7 +442,24 @@ cdef class Letter(Element):
             True
             sage: C(4) == C(4)
             True
+
+        TESTS::
+
+            sage: C = CrystalOfLetters(['C', 3])
+            sage: C('E') == C(2)
+            False
+            sage: C(2) == C('E')
+            False
+            sage: C('E') == C('E')
+            True
         """
+        # Special case for the empty letter
+        if isinstance(left, EmptyLetter):
+            return isinstance(right, EmptyLetter) \
+                   and (op == Py_EQ or op == Py_LE or op == Py_GE)
+        if isinstance(right, EmptyLetter):
+            return op == Py_NE
+
         cdef Letter self, x
         self = left
         x = right
@@ -462,11 +479,42 @@ cdef class Letter(Element):
 
 cdef class EmptyLetter(Element):
     """
-    The (affine) letter `\emptyset` thought of as a classical crystal letter
+    The affine)letter `\emptyset` thought of as a classical crystal letter
     in classical type `B_n` and `C_n`.
 
+    .. WARNING::
+
+        This is not a classical letter.
+
     Used in the rigged configuration bijections.
     """
+    cdef readonly str value
+
+    def __init__(self, parent):
+        """
+        Initialize ``xelf``.
+
+        EXAMPLES::
+
+            sage: C = CrystalOfLetters(['C', 3])
+            sage: TestSuite(C('E')).run()
+        """
+        self.value = 'E'
+        Element.__init__(self, parent)
+
+    def __reduce__(self):
+        r"""
+        Used in pickling crystal of letters elements.
+
+        EXAMPLES::
+
+            sage: C = CrystalOfLetters(['C',3])
+            sage: a = C('E')
+            sage: a.__reduce__()
+            (The crystal of letters for type ['C', 3], ('E',))
+        """
+        return (self._parent, ('E',))
+
     def _repr_(self):
         """
         Return a string representation of ``self``.
@@ -491,6 +539,18 @@ cdef class EmptyLetter(Element):
         """
         return "\\emptyset"
 
+    def __hash__(self):
+        """
+        Return the hash value of ``self``.
+
+        EXAMPLES::
+
+            sage: C = CrystalOfLetters(['D', 4])
+            sage: hash(C('E')) == hash('E')
+            True
+        """
+        return hash(self.value)
+
     def weight(self):
         """
         Return the weight of ``self``.
@@ -514,7 +574,16 @@ cdef class EmptyLetter(Element):
         """
         return None
 
-    f = e
+    cpdef f(self, int i):
+        """
+        Return `f_i` of ``self`` which is ``None``.
+
+        EXAMPLES::
+
+            sage: C = CrystalOfLetters(['C', 3])
+            sage: C('E').f(1)
+        """
+        return None
 
     cpdef int epsilon(self, int i):
         r"""
@@ -528,7 +597,17 @@ cdef class EmptyLetter(Element):
         """
         return 0
 
-    phi = epsilon
+    cpdef int phi(self, int i):
+        r"""
+        Return `\varphi_i` of ``self``.
+
+        EXAMPLES::
+
+            sage: C = CrystalOfLetters(['C', 3])
+            sage: C('E').phi(1)
+            0
+        """
+        return 0
 
 #########################
 # Type A

src/sage/combinat/rigged_configurations/all.py

@@ -1,6 +1,4 @@
-from rigged_configurations import HighestWeightRiggedConfigurations
 from rigged_configurations import RiggedConfigurations
-from tensor_product_kr_tableaux import HighestWeightTensorProductOfKirillovReshetikhinTableaux
 from tensor_product_kr_tableaux import TensorProductOfKirillovReshetikhinTableaux
 from kr_tableaux import KirillovReshetikhinTableaux