On representations of Lie algebras compatible with a grading

Details On representations of Lie algebras compatible with a grading On representations of Lie algebras compatible with a grading

2009-01-15

arxiv.org/abs/0901.2300v1

Acta Polytechnica 50 (2010) No.5, 30-39 [ISSN 1210/2709]

Physics

Mathematical Physics

15 pages

Scientific paper

The paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is defined and applied to finite-dimensional representations of $sl(n,\mathbb{C})$ in relation with its $\mathbb{Z}_2$-gradings. For representation theory of $sl(n,\mathbb{C})$ the Gel'fand-Tseitlin method turned out very effective.

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