A theory of grading preserving contractions of representations of Lie algebras has been developed. In this theory, grading of the given Lie algebra is characterized by two sets of parameters satisfying a derived set of equations. Here we introduce a list of resulting 3-dimensional representations for the $\mathbb{Z}_3$-grading of the $\mathfrak{sl}(2)$ Lie algebra.
J. Gen. Lie Theory Appl.
6:
1-6
(2012).
DOI: 10.4303/jglta/G110902