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r"""
Bijection between rigged configurations and KR tableaux
Functions which are big switch statements to create the bijection class of the
correct type.
AUTHORS:
- Travis Scrimshaw (2011-04-15): Initial version
- Travis Scrimshaw (2012-12-21): Added all non-exceptional bijection types
- Travis Scrimshaw (2014-09-10): Added type `D_4^{(3)}`
"""
#*****************************************************************************
# Copyright (C) 2011-2015 Travis Scrimshaw <tscrim@ucdavis.edu>
#
# Distributed under the terms of the GNU General Public License (GPL)
#
# This code is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# The full text of the GPL is available at:
#
# http://www.gnu.org/licenses/
#*****************************************************************************
from sage.combinat.rigged_configurations.bij_type_A import KRTToRCBijectionTypeA
from sage.combinat.rigged_configurations.bij_type_A import RCToKRTBijectionTypeA
from sage.combinat.rigged_configurations.bij_type_B import KRTToRCBijectionTypeB
from sage.combinat.rigged_configurations.bij_type_B import RCToKRTBijectionTypeB
from sage.combinat.rigged_configurations.bij_type_C import KRTToRCBijectionTypeC
from sage.combinat.rigged_configurations.bij_type_C import RCToKRTBijectionTypeC
from sage.combinat.rigged_configurations.bij_type_D import KRTToRCBijectionTypeD
from sage.combinat.rigged_configurations.bij_type_D import RCToKRTBijectionTypeD
from sage.combinat.rigged_configurations.bij_type_D_twisted import KRTToRCBijectionTypeDTwisted
from sage.combinat.rigged_configurations.bij_type_D_twisted import RCToKRTBijectionTypeDTwisted
from sage.combinat.rigged_configurations.bij_type_A2_even import KRTToRCBijectionTypeA2Even
from sage.combinat.rigged_configurations.bij_type_A2_even import RCToKRTBijectionTypeA2Even
from sage.combinat.rigged_configurations.bij_type_A2_dual import KRTToRCBijectionTypeA2Dual
from sage.combinat.rigged_configurations.bij_type_A2_dual import RCToKRTBijectionTypeA2Dual
from sage.combinat.rigged_configurations.bij_type_A2_odd import KRTToRCBijectionTypeA2Odd
from sage.combinat.rigged_configurations.bij_type_A2_odd import RCToKRTBijectionTypeA2Odd
from sage.combinat.rigged_configurations.bij_type_D_tri import KRTToRCBijectionTypeDTri
from sage.combinat.rigged_configurations.bij_type_D_tri import RCToKRTBijectionTypeDTri
from sage.combinat.rigged_configurations.bij_type_E67 import KRTToRCBijectionTypeE67
from sage.combinat.rigged_configurations.bij_type_E67 import RCToKRTBijectionTypeE67
def KRTToRCBijection(tp_krt):
r"""
Return the correct KR tableaux to rigged configuration bijection helper class.
TESTS::
sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(['A', 4, 1], [[2,1]])
sage: from sage.combinat.rigged_configurations.bijection import KRTToRCBijection
sage: bijection = KRTToRCBijection(KRT(pathlist=[[5,2]]))
"""
ct = tp_krt.cartan_type()
typ = ct.type()
if ct.is_untwisted_affine():
if typ == 'A':
return KRTToRCBijectionTypeA(tp_krt)
if typ == 'B':
return KRTToRCBijectionTypeB(tp_krt)
if typ == 'C':
return KRTToRCBijectionTypeC(tp_krt)
if typ == 'D':
return KRTToRCBijectionTypeD(tp_krt)
if typ == 'E':
if ct.classical().rank() < 8:
return KRTToRCBijectionTypeE67(tp_krt)
#if typ == 'F':
#if typ == 'G':
else:
if typ == 'BC': # A_{2n}^{(2)}
return KRTToRCBijectionTypeA2Even(tp_krt)
typ = ct.dual().type()
if typ == 'BC': # A_{2n}^{(2)\dagger}
return KRTToRCBijectionTypeA2Dual(tp_krt)
if typ == 'B': # A_{2n-1}^{(2)}
return KRTToRCBijectionTypeA2Odd(tp_krt)
if typ == 'C': # D_{n+1}^{(2)}
return KRTToRCBijectionTypeDTwisted(tp_krt)
#if typ == 'F': # E_6^{(2)}
if typ == 'G': # D_4^{(3)}
return KRTToRCBijectionTypeDTri(tp_krt)
raise NotImplementedError
def RCToKRTBijection(rigged_configuration_elt):
r"""
Return the correct rigged configuration to KR tableaux bijection helper class.
TESTS::
sage: RC = RiggedConfigurations(['A', 4, 1], [[2, 1]])
sage: from sage.combinat.rigged_configurations.bijection import RCToKRTBijection
sage: bijection = RCToKRTBijection(RC(partition_list=[[1],[1],[1],[1]]))
"""
ct = rigged_configuration_elt.cartan_type()
typ = ct.type()
if not ct.is_affine() or ct.is_untwisted_affine():
if typ == 'A':
return RCToKRTBijectionTypeA(rigged_configuration_elt)
if typ == 'B':
return RCToKRTBijectionTypeB(rigged_configuration_elt)
if typ == 'C':
return RCToKRTBijectionTypeC(rigged_configuration_elt)
if typ == 'D':
return RCToKRTBijectionTypeD(rigged_configuration_elt)
if typ == 'E':
if ct.classical().rank() < 8:
return RCToKRTBijectionTypeE67(rigged_configuration_elt)
#if typ == 'F':
#if typ == 'G':
else:
if typ == 'BC': # A_{2n}^{(2)}
return RCToKRTBijectionTypeA2Even(rigged_configuration_elt)
typ = ct.dual().type()
if typ == 'BC': # A_{2n}^{(2)\dagger}
return RCToKRTBijectionTypeA2Dual(rigged_configuration_elt)
if typ == 'B': # A_{2n-1}^{(2)}
return RCToKRTBijectionTypeA2Odd(rigged_configuration_elt)
if typ == 'C': # D_{n+1}^{(2)}
return RCToKRTBijectionTypeDTwisted(rigged_configuration_elt)
#if typ == 'F': # E_6^{(2)}
if typ == 'G': # D_4^{(3)}
return RCToKRTBijectionTypeDTri(rigged_configuration_elt)
raise NotImplementedError
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