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""" Root Systems ============
Quickref --------
- ``T = CartanType(["A", 3]), T.is_finite()`` -- Cartan types - ``T.dynkin_diagram(), DynkinDiagram(["G",2])`` -- Dynkin diagrams - ``T.cartan_matrix(), CartanMatrix(["F",4])`` -- Cartan matrices - ``RootSystem(T).weight_lattice()`` -- Root systems - ``WeylGroup(["B", 6, 1]).simple_reflections()`` -- Affine Weyl groups - ``WeylCharacterRing(["D", 4])`` -- Weyl character rings
Introductory material ---------------------
- :ref:`sage.combinat.root_system` -- This overview - :class:`CartanType` -- An introduction to Cartan types - :class:`RootSystem` -- An introduction to root systems - :ref:`sage.combinat.root_system.plot` -- A root system visualization tutorial
- The `Lie Methods and Related Combinatorics <../../../../../thematic_tutorials/lie.html>`_ thematic tutorial
Related material ----------------
- :ref:`sage.combinat.crystals` -- Crystals
Cartan datum ------------
- :ref:`sage.combinat.root_system.cartan_type` - :ref:`sage.combinat.root_system.dynkin_diagram` - :ref:`sage.combinat.root_system.cartan_matrix` - :ref:`sage.combinat.root_system.coxeter_matrix` - :ref:`sage.combinat.root_system.coxeter_type`
Root systems ------------
- :ref:`sage.combinat.root_system.root_system` - :ref:`sage.combinat.root_system.plot` - :ref:`sage.combinat.root_system.root_lattice_realizations` - :ref:`sage.combinat.root_system.root_lattice_realization_algebras` - :ref:`sage.combinat.root_system.weight_lattice_realizations` - :ref:`sage.combinat.root_system.root_space` - :ref:`sage.combinat.root_system.weight_space` - :ref:`sage.combinat.root_system.ambient_space`
Coxeter groups --------------
- :ref:`sage.combinat.root_system.coxeter_group` - :ref:`sage.combinat.root_system.weyl_group` - :ref:`sage.combinat.root_system.extended_affine_weyl_group` - :ref:`sage.combinat.root_system.fundamental_group` - :ref:`sage.combinat.root_system.braid_move_calculator`
.. SEEALSO::
The categories :class:`CoxeterGroups` and :class:`WeylGroups`
Finite reflection groups ------------------------
- :ref:`sage.combinat.root_system.reflection_group_complex` - :ref:`sage.combinat.root_system.reflection_group_real`
.. SEEALSO::
The category :class:`~sage.categories.complex_reflection_groups.ComplexReflectionGroups`
Representation theory ---------------------
- :ref:`sage.combinat.root_system.weyl_characters` - :ref:`sage.combinat.root_system.integrable_representations` - :ref:`sage.combinat.root_system.branching_rules` - :ref:`sage.combinat.root_system.hecke_algebra_representation` - :ref:`sage.combinat.root_system.non_symmetric_macdonald_polynomials`
Root system data and code for specific families of Cartan types ---------------------------------------------------------------
- :ref:`sage.combinat.root_system.type_affine` - :ref:`sage.combinat.root_system.type_dual` - :ref:`sage.combinat.root_system.type_folded` - :ref:`sage.combinat.root_system.type_reducible` - :ref:`sage.combinat.root_system.type_relabel` - :ref:`sage.combinat.root_system.type_marked`
Root system data and code for specific Cartan types ---------------------------------------------------
- :ref:`sage.combinat.root_system.type_A` - :ref:`sage.combinat.root_system.type_B` - :ref:`sage.combinat.root_system.type_C` - :ref:`sage.combinat.root_system.type_D` - :ref:`sage.combinat.root_system.type_E` - :ref:`sage.combinat.root_system.type_F` - :ref:`sage.combinat.root_system.type_G` - :ref:`sage.combinat.root_system.type_H` - :ref:`sage.combinat.root_system.type_I` - :ref:`sage.combinat.root_system.type_A_affine` - :ref:`sage.combinat.root_system.type_B_affine` - :ref:`sage.combinat.root_system.type_C_affine` - :ref:`sage.combinat.root_system.type_D_affine` - :ref:`sage.combinat.root_system.type_E_affine` - :ref:`sage.combinat.root_system.type_F_affine` - :ref:`sage.combinat.root_system.type_G_affine` - :ref:`sage.combinat.root_system.type_BC_affine` - :ref:`sage.combinat.root_system.type_super_A` - :ref:`sage.combinat.root_system.type_A_infinity` """ # currently needed to activate the backward compatibility # register_unpickle_override from . import type_A from . import type_B from . import type_C from . import type_D from . import type_E from . import type_F from . import type_G |