In this talk, we introduce monomial irreducible representations of the special linear Lie algebra sln(C). We will show that, this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula. Let L be a finite dimensional complex simple Lie algebra. For any functional integral dominant weight ?, we denote the associated irreducible module byL(?). One of the most important problems concerning representations of simple Lie algebras, is considered in this talk: to find an ordered basis for L(?), such that one can obtain the matrix representations of elements of L with respect to this ordered basis. It is trivial that handling with matrix representations are more flexible than working with L-modules, especially in practise.