Crystal base
Representation of a quantum group / From Wikipedia, the free encyclopedia
Not to be confused with crystal (mathematics).
A crystal base for a representation of a quantum group on a -vector space
is not a base of that vector space but rather a
-base of
where
is a
-lattice in that vector space. Crystal bases appeared in the work of Kashiwara (1990) and also in the work of Lusztig (1990). They can be viewed as specializations as
of the canonical basis defined by Lusztig (1990).