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

M. Havlíček, E. Pelantová, J. Tolar

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.


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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague