Let be a CartanType with index set
, and
be
the corresponding weight lattice of the type
. Let
and
denote the corresponding simple roots
and coroots respectively. Let us give the axiomatic definition
of a crystal.
A type crystal
is a non-empty set with maps
,
, and
for
satisfying the following properties for all
:
This is a catalog of crystals that are currently in Sage:
Functorial constructions:
Subcatalogs: