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
- run()#
Run the bijection from a marginally large tableaux to a rigged configuration.
EXAMPLES:
sage: vct = CartanType(['B',4]).as_folding() sage: RC = crystals.infinity.RiggedConfigurations(vct) 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
- 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
- run()#
Run the bijection from rigged configurations to a marginally large tableau.
EXAMPLES:
sage: vct = CartanType(['B',4]).as_folding() sage: RC = crystals.infinity.RiggedConfigurations(vct) 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
- 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