Finite Crystals

class sage.categories.finite_crystals.FiniteCrystals(base_category)

Bases: CategoryWithAxiom_singleton

The category of finite crystals.

EXAMPLES:

Sage

sage: C = FiniteCrystals()
sage: C
Category of finite crystals
sage: C.super_categories()
[Category of crystals, Category of finite enumerated sets]
sage: C.example()
Highest weight crystal of type A_3 of highest weight omega_1

Python

>>> from sage.all import *
>>> C = FiniteCrystals()
>>> C
Category of finite crystals
>>> C.super_categories()
[Category of crystals, Category of finite enumerated sets]
>>> C.example()
Highest weight crystal of type A_3 of highest weight omega_1

class TensorProducts(category, *args)

Bases: TensorProductsCategory

The category of finite crystals constructed by tensor product of finite crystals.

extra_super_categories()

EXAMPLES:

Sage

sage: FiniteCrystals().TensorProducts().extra_super_categories()
[Category of finite crystals]

Python

>>> from sage.all import *
>>> FiniteCrystals().TensorProducts().extra_super_categories()
[Category of finite crystals]

example(n=3)

Return an example of highest weight crystals, as per Category.example().

EXAMPLES:

Sage

sage: B = FiniteCrystals().example(); B
Highest weight crystal of type A_3 of highest weight omega_1

Python

>>> from sage.all import *
>>> B = FiniteCrystals().example(); B
Highest weight crystal of type A_3 of highest weight omega_1

extra_super_categories()

EXAMPLES:

Sage

sage: FiniteCrystals().extra_super_categories()
[Category of finite enumerated sets]

Python

>>> from sage.all import *
>>> FiniteCrystals().extra_super_categories()
[Category of finite enumerated sets]