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.
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.

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.

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()
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
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()
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
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()
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
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()
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