On Representations of sl(n, C) Compatible with a Z2-grading

Abstract

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.