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This paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is applied to finite-dimensional representations of sl(n,C) in relation to its Z2-gradings. For representation theory of sl(n,C) the Gel'fand-Tseitlin method turned out very efficient. We show that it is not generally true that every irreducible representation can be compatibly graded.doaj:1e37fb4cb4f14851a3f09a0f261f964f fatcat:muo3zp6zmrhorefvjkyaddnrb4