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[source]#

Bases: Morphism

Crystal isomorphism of \(B(\infty)\) in the rigged configuration model to the tableau model.

class sage.combinat.rigged_configurations.bij_infinity.FromTableauIsomorphism[source]#

Bases: 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)[source]#

Bases: KRTToRCBijectionTypeB

run()[source]#

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

>>> from sage.all import *
>>> vct = CartanType(['B',Integer(4)]).as_folding()
>>> RC = crystals.infinity.RiggedConfigurations(vct)
>>> T = crystals.infinity.Tableaux(['B',Integer(4)])
>>> Psi = T.crystal_morphism({T.module_generators[Integer(0)]: RC.module_generators[Integer(0)]})
>>> TS = [x.value for x in T.subcrystal(max_depth=Integer(4))]
>>> all(Psi(b) == RC(b) for b in TS) # long time # indirect doctest
True
class sage.combinat.rigged_configurations.bij_infinity.MLTToRCBijectionTypeD(tp_krt)[source]#

Bases: KRTToRCBijectionTypeD

run()[source]#

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

>>> from sage.all import *
>>> RC = crystals.infinity.RiggedConfigurations(['D',Integer(4)])
>>> T = crystals.infinity.Tableaux(['D',Integer(4)])
>>> Psi = T.crystal_morphism({T.module_generators[Integer(0)]: RC.module_generators[Integer(0)]})
>>> TS = [x.value for x in T.subcrystal(max_depth=Integer(4))]
>>> all(Psi(b) == RC(b) for b in TS) # long time # indirect doctest
True
class sage.combinat.rigged_configurations.bij_infinity.RCToMLTBijectionTypeB(RC_element)[source]#

Bases: RCToKRTBijectionTypeB

run()[source]#

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

>>> from sage.all import *
>>> vct = CartanType(['B',Integer(4)]).as_folding()
>>> RC = crystals.infinity.RiggedConfigurations(vct)
>>> T = crystals.infinity.Tableaux(['B',Integer(4)])
>>> Psi = RC.crystal_morphism({RC.module_generators[Integer(0)]: T.module_generators[Integer(0)]})
>>> RCS = [x.value for x in RC.subcrystal(max_depth=Integer(4))]
>>> all(Psi(nu) == T(nu) for nu in RCS) # long time # indirect doctest
True
class sage.combinat.rigged_configurations.bij_infinity.RCToMLTBijectionTypeD(RC_element)[source]#

Bases: RCToKRTBijectionTypeD

run()[source]#

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

>>> from sage.all import *
>>> RC = crystals.infinity.RiggedConfigurations(['D',Integer(4)])
>>> T = crystals.infinity.Tableaux(['D',Integer(4)])
>>> Psi = RC.crystal_morphism({RC.module_generators[Integer(0)]: T.module_generators[Integer(0)]})
>>> RCS = [x.value for x in RC.subcrystal(max_depth=Integer(4))]
>>> all(Psi(nu) == T(nu) for nu in RCS) # long time # indirect doctest
True