Bijection between rigged configurations for \(B(\infty)\) and marginally large tableaux¶
AUTHORS:
- Travis Scrimshaw (2015-07-01): Initial version
REFERENCES:
[RC-MLT] | Ben Salisbury and Travis Scrimshaw. Connecting marginally large tableaux and rigged configurations via crystals. Preprint. Arxiv 1505.07040. |
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class
sage.combinat.rigged_configurations.bij_infinity.
FromRCIsomorphism
¶ Bases:
sage.categories.morphism.Morphism
Crystal isomorphism of \(B(\infty)\) in the rigged configuration model to the tableau model.
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class
sage.combinat.rigged_configurations.bij_infinity.
FromTableauIsomorphism
¶ Bases:
sage.categories.morphism.Morphism
Crystal isomorphism of \(B(\infty)\) in the tableau model to the rigged configuration model.
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class
sage.combinat.rigged_configurations.bij_infinity.
MLTToRCBijectionTypeB
(tp_krt)¶ Bases:
sage.combinat.rigged_configurations.bij_type_B.KRTToRCBijectionTypeB
Initialize the bijection by obtaining the important information from the KR tableaux.
INPUT:
parent
– The parent of tensor product of KR tableaux
EXAMPLES:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[3,1]])) sage: TestSuite(bijection).run()
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run
()¶ Run the bijection from a marginally large tableaux to a rigged configuration.
EXAMPLES:
sage: RC = crystals.infinity.RiggedConfigurations(['B',4]) sage: T = crystals.infinity.Tableaux(['B',4]) sage: Psi = T.crystal_morphism({T.module_generators[0]: RC.module_generators[0]}) sage: TS = [x.value for x in T.subcrystal(max_depth=4)] sage: all(Psi(b) == RC(b) for b in TS) # long time # indirect doctest True
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class
sage.combinat.rigged_configurations.bij_infinity.
MLTToRCBijectionTypeD
(tp_krt)¶ Bases:
sage.combinat.rigged_configurations.bij_type_D.KRTToRCBijectionTypeD
Initialize the bijection by obtaining the important information from the KR tableaux.
INPUT:
parent
– The parent of tensor product of KR tableaux
EXAMPLES:
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]]) sage: from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA sage: bijection = KRTToRCBijectionTypeA(KRT(pathlist=[[3,1]])) sage: TestSuite(bijection).run()
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run
()¶ Run the bijection from a marginally large tableaux to a rigged configuration.
EXAMPLES:
sage: RC = crystals.infinity.RiggedConfigurations(['D',4]) sage: T = crystals.infinity.Tableaux(['D',4]) sage: Psi = T.crystal_morphism({T.module_generators[0]: RC.module_generators[0]}) sage: TS = [x.value for x in T.subcrystal(max_depth=4)] sage: all(Psi(b) == RC(b) for b in TS) # long time # indirect doctest True
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class
sage.combinat.rigged_configurations.bij_infinity.
RCToMLTBijectionTypeB
(RC_element)¶ Bases:
sage.combinat.rigged_configurations.bij_type_B.RCToKRTBijectionTypeB
Initialize the bijection helper.
INPUT:
RC_element
– The rigged configuration
EXAMPLES:
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_abstract_class import RCToKRTBijectionAbstract sage: bijection = RCToKRTBijectionAbstract(RC(partition_list=[[1],[1],[1],[1]])) sage: TestSuite(bijection).run()
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run
()¶ Run the bijection from rigged configurations to a marginally large tableau.
EXAMPLES:
sage: RC = crystals.infinity.RiggedConfigurations(['B',4]) sage: T = crystals.infinity.Tableaux(['B',4]) sage: Psi = RC.crystal_morphism({RC.module_generators[0]: T.module_generators[0]}) sage: RCS = [x.value for x in RC.subcrystal(max_depth=4)] sage: all(Psi(nu) == T(nu) for nu in RCS) # long time # indirect doctest True
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class
sage.combinat.rigged_configurations.bij_infinity.
RCToMLTBijectionTypeD
(RC_element)¶ Bases:
sage.combinat.rigged_configurations.bij_type_D.RCToKRTBijectionTypeD
Initialize the bijection helper.
INPUT:
RC_element
– The rigged configuration
EXAMPLES:
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]]) sage: from sage.combinat.rigged_configurations.bij_abstract_class import RCToKRTBijectionAbstract sage: bijection = RCToKRTBijectionAbstract(RC(partition_list=[[1],[1],[1],[1]])) sage: TestSuite(bijection).run()
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run
()¶ Run the bijection from rigged configurations to a marginally large tableau.
EXAMPLES:
sage: RC = crystals.infinity.RiggedConfigurations(['D',4]) sage: T = crystals.infinity.Tableaux(['D',4]) sage: Psi = RC.crystal_morphism({RC.module_generators[0]: T.module_generators[0]}) sage: RCS = [x.value for x in RC.subcrystal(max_depth=4)] sage: all(Psi(nu) == T(nu) for nu in RCS) # long time # indirect doctest True